Vibration damping device and elevator apparatus

ABSTRACT

An object of the present invention is to provide a vibration damping device including an instability preventing means, for efficiently suppressing amplification of vibration of a long structure, which is mechanically flexible, due to a resonance phenomenon. A vibration damping device ( 100 ) for reducing vibration of a long structure ( 1 ) includes a displacement amplifier ( 7 ) and limiting members ( 8 ). The displacement amplifier ( 7 ) is arranged along a given position in the longitudinal direction of the structure ( 1 ). The displacement amplifier ( 7 ) amplifies a displacement of the structure ( 1 ). The limiting members ( 8 ) control displacement amplification performed by the displacement amplifier ( 7 ) such that the displacement of the structure ( 1 ) amplified by the displacement amplifier ( 7 ) does not become greater than a first displacement, the first displacement being a displacement of the structure ( 1 ) by which the structure ( 1 ) is not allowed to return to the equilibrium position of the vibration.

FIELD

The present invention relates to a vibration damping device to controlvibration of a long structure.

BACKGROUND

As a vibration damping device for an elevator rope, for example, thereis disclosed a conventional vibration damping device that includes adamper (which converts vibration energy into heat energy and dissipatesthe energy) disposed in a machine room located near an end of theelevator rope, for controlling vibration of the elevator rope (PTL 1).

As another vibration damping device, there is also disclosed a devicethat is disposed near an end of a rope and includes a mechanical elementfor applying a negative centering force to an elevator rope in the samedirection as the displacement direction of the elevator rope, and alsoincludes an inverted pendulum to implement the negative centering force(PTL 2). Meanwhile, there is also disclosed the use of the attractionforce of a permanent magnet to implement such a negative centering force(PTL 3).

CITATION LIST Patent Literature

[PTL 1] JP 2007-1711 A

[PTL 2] JP H3-26682 A

[PTL 3] JP 2007-309411 A

SUMMARY Technical Problem

In the conventional vibration damping device, a damper is provided at aportion where the amplitude of a long structure is small. Thus, theobtained vibration damping effect is small, and it may be impossible toprovide the damper at a portion where the amplitude is large. Further,since negative stiffness obtained with an inverted pendulum or apermanent magnet has a property such that its stiffness value increasesnonlinearly with an increase in displacement of a long structure, thenegative stiffness would become excessively large and become unstable ifthe displacement of the long structure is increased. Then, thedisplacement of the vibration damping device would be fixed at themaximum position of the range of motion of the vibration dampingmechanism, which is problematic in that the vibration damping effect ofthe negative stiffness cannot be exhibited.

It is an object of the present invention to provide a vibration dampingdevice including an instability preventing means, for efficientlysuppressing amplification of vibration of a long structure, which ismechanically flexible, due to a resonance phenomenon.

Solution to Problem

A vibration damping device according to the present invention forreducing vibration of a long structure, includes: a displacementamplifier arranged along a given position in a longitudinal direction ofthe structure, the displacement amplifier being configured to amplify adisplacement of the structure; and a limiting member that controlsdisplacement amplification performed by the displacement amplifier suchthat the displacement of the structure amplified by the displacementamplifier does not become greater than a first displacement, the firstdisplacement being the displacement of the structure by which thestructure is not allowed to return to an equilibrium position of thevibration.

An elevator apparatus according to the present invention includes theaforementioned vibration damping device.

Advantageous Effects of Invention

According to the present invention, it is possible to perform vibrationcontrol while preventing instability using a vibration damping deviceprovided at a given position along a long structure.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic view of the long structure according to Embodiment1.

FIG. 2 is a schematic view illustrating the state of vibration of thelong structure according to Embodiment 1.

FIG. 3 are schematic views in which vibration of the long structureaccording to Embodiment 1 is controlled with a damper.

FIG. 4 is a view illustrating the displacement amplifier provided to along structure according to Embodiment 1.

FIG. 5 is a graph illustrating an unstable phenomenon of the vibrationdamping device.

FIG. 6 is a graph illustrating the concept of preventing unstableoperation of the vibration damping device.

FIG. 7 are views each illustrating limiting members of the vibrationdamping device according to Embodiment 1.

FIG. 8 is a view illustrating the vibration damping device with thedamper according to Embodiment 1.

FIG. 9 are views illustrating the configuration and the effect of thevibration damping device according to Embodiment 1.

FIG. 10 are views illustrating an example in which the vibration dampingdevice according to Embodiment 1 is applied to the structure having nofixed plane at either end thereof.

FIG. 11 are views each illustrating an example in which the vibrationdamping device according to Embodiment 1 is not connected to anythingother than the structure, and both ends of the vibration damping deviceare coupled to the structure.

FIG. 12 is a view illustrating the elevator apparatus according toEmbodiment 2.

FIG. 13 is a view illustrating the time when the elevator apparatusaccording to Embodiment 2 is vibrated.

FIG. 4 is a view illustrating the vibration damping device of theelevator apparatus according to Embodiment 2.

FIG. 15 is a view of the vibration damping device with limiting membersof the elevator apparatus according to Embodiment 2.

FIG. 16 is a view of the vibration damping device according toEmbodiment 2 provided in the rope duct.

FIG. 17 is a front view illustrating the vibration damping device withthe negative stiffness porsion configured with the link mechanism of theelevator apparatus according to Embodiment 2.

FIG. 18 is a top view illustrating the vibration damping device with thenegative stiffness porsion configured with the link mechanism of theelevator apparatus according to Embodiment 2.

FIG. 19 is a graph illustrates the relation between the ratio of thedistance from the end to the position where vibration damping device isprovided to the length of the main rope of the elevator apparatusaccording to Embodiment 2 and the maximum damping ratio.

FIG. 20 is a graph illustrates the relation between the normalizedstiffness value when positive or negative stiffness is applied to theelevator apparatus according to Embodiment 2 and the maximum dampingratio.

FIG. 21 is a view illustrates an exemplary configuration of thevibration damping device that controls longitudinal vibration in of theelevator apparatus according to Embodiment 2.

FIG. 22 is a perspective view of the vibration damping device accordingto Embodiment 2.

FIG. 23 are views each illustrating the relation between the position ofthe car of the elevator apparatus according to Embodiment 2 and thefleet angle.

FIG. 24 is a perspective view of the vibration damping device accordingto Embodiment 2.

FIG. 25 is a perspective view of the vibration damping device accordingto Embodiment 2.

FIG. 26 is a top view of the vibration damping device according toEmbodiment 2.

FIG. 27 is a side view of the vibration damping device according toEmbodiment 2.

FIG. 28 is a side view of the vibration damping device according toEmbodiment 2.

FIG. 29 is a schematic view of the elevator apparatus according toEmbodiment 2.

FIG. 30 are side views of the vibration damping device according toEmbodiment 2.

FIG. 31 is a configuration view of the elevator apparatus according toEmbodiment 3.

FIG. 32 is a configuration view of the elevator apparatus according toEmbodiment 3.

FIG. 33 is a side view of the vibration damping device according toEmbodiment 3.

FIG. 34 are side views of the vibration damping device according toEmbodiment 3.

FIG. 35 is a side view of the vibration damping device according toEmbodiment 3.

FIG. 36 is a side view of the vibration damping device according toEmbodiment 3.

FIG. 37 are side views of the vibration damping device according toEmbodiment 3.

FIG. 38 is a side view of the vibration damping device according toEmbodiment 3.

FIG. 39 is a side view of the vibration damping device according toEmbodiment 3.

FIG. 40 are a side view of the vibration damping device according toEmbodiment 3.

FIG. 41 is a side view of the vibration damping device according toEmbodiment 3.

FIG. 42 is a perspective view of the vibration damping device accordingto Embodiment 3.

FIG. 43 is a top view of the vibration damping device according toEmbodiment 3.

FIG. 44 is a perspective view of the vibration damping device accordingto Embodiment 3.

FIG. 45 is a side view of the vibration damping device according toEmbodiment 3.

FIG. 46 is a top view of the vibration damping device according toEmbodiment 3.

FIG. 47 is a side view of the vibration damping device according toEmbodiment 3.

FIG. 48 is a perspective view of the vibration damping device accordingto Embodiment 3.

FIG. 49 is a perspective view of the vibration damping device accordingto Embodiment 3.

FIG. 50 is a top view of the vibration damping device according toEmbodiment 3.

FIG. 51 is a top view of the vibration damping device according toEmbodiment 3.

FIG. 52 are configuration views of the elevator apparatus according toEmbodiment 3.

FIG. 53 is a side view of the vibration damping device according toEmbodiment 3.

FIG. 54 are configuration views of the elevator apparatus according toEmbodiment 3.

DESCRIPTION OF EMBODIMENTS Embodiment 1

Embodiment 1 will be described with reference to the drawings. It shouldbe noted that the present invention is not limited to the specificexamples described hereinafter, and the dimensions, materials, andshapes can be changed as appropriate.

FIG. 1 is a schematic view of a structure 1 that is a vibration controltarget of a vibration damping device 100 of the present embodiment. Thestructure 1 herein is a long object having a longer dimension at leastalong one direction thereof than that along the other direction. Thestructure 1 may be a bar-like or plate-like structure or a rope-likeobject, for example. Alternatively, the structure 1 may be a structuralmember that supports something to maintain its shape, or a flexiblemember whose shape will greatly change against turbulence. In addition,the structure 1 may be fixed to another object at a given position alongthe direction of its longer dimension.

The structure 1 is fixed at both ends to fixed planes 2 a and 2 b. Thefigure illustrates the x-axis, y-axis, and z-axis of the 3-axisorthogonal coordinate system, and the vertically upward directioncorresponds to the positive direction of the z-axis. The longitudinaldirection of the structure 1 is parallel with the z-axis, and thus, thestructure 1 is arranged along the vertical direction. The fixed plane 2a is located above the structure 1 in the vertical direction, and thefixed plane 2 b is located below the structure 1 in the verticaldirection. FIG. 1 illustrates a state in which the structure 1 is notvibrated and thus vibration in the transverse direction that is adirection perpendicular to the longitudinal direction (hereinafterreferred to as “transverse vibration”) is not generated.

FIG. 2 is a schematic view illustrating the state of a structure 1 athat is vibrated. In FIG. 1, when a vibration force 3 to vibrate thefixed plane 2 a is applied to the fixed plane 2 a and the vibrationfrequency of the vibration force 3 coincides with the natural frequencyof the structure 1 a, a resonance phenomenon occurs. Then, the amplitudeof the structure 1 a (and the fixed plane 2 a) is amplified. Althoughthe figure illustrates that the direction of the vibration of thevibration force 3 and the structure 1 a is the y-axis direction, thepresent invention is not limited thereto, and the same holds true forany direction on the xy plane. In addition, a similar phenomenon occurswhen the fixed plane 2 b is vibrated.

Herein, the amplitude of vibration when resonance of the structure 1 aoccurs differs depending on the position of the structure 1 a in thelongitudinal direction (i.e., z-direction), and is determined by thedistribution of the stiffness and mass of the structure 1 a.

FIG. 3 are schematic views in which vibration (or resonant vibration) ofthe structure 1 a is controlled with a damper. Herein, the damper is aviscous element that converts vibration energy into heat energy by meansof viscous resistance or friction, for example, and dissipates theenergy, thereby absorbing the vibration, and exerts a force proportionalto speed. FIG. 3(a) illustrates disposing a damper 4 as a vibrationdamping means via a fixed plane 2 c at a position away from the fixedplane 2 b by a distance 5 a in the vertically upward direction (i.e.,z-direction). In contrast, in FIG. 3(b), the damper 4 is disposed at aposition away from the fixed plane 2 b by a distance 5 b, which isgreater than the distance 5 a and is half the longitudinal length of thestructure 1, in the vertically upward direction (i.e., z-direction).

When the amplitude of vibration of the structure 1 a at the positionwhere the damper 4 is disposed in FIG. 3(a) is compared with that inFIG. 3(b), it is found that an amplitude 6 a in FIG. 3(a) at a positioncloser to the fixed plane 2 b is smaller than an amplitude 6 b in FIG.3(b). Then, since the displacement of the damper 4 in FIG. 3(a) issmaller than that in FIG. 3(b), the vibration damping effect of thedamper 4 in FIG. 3(a) is smaller than that in FIG. 3(b).

However, since the position where the damper 4 of FIG. 3(a) is disposedis close to the fixed plane 2 b, its installation is easier than that ofthe damper 4 in FIG. 3(b). Therefore, the damper 4 is disposed at aposition near the fixed plane 2 b where its installation is easy, and adevice for increasing the vibration damping effect of the damper 4 isintroduced. Although the configuration illustrated herein is intended toincrease the vibration damping effect of the damper 4, a deviceconfiguration without the damper 4 is also possible.

Other than the aforementioned damper 4, as a conventional vibrationdamping device, there is also known a vibration damping device that usesan inverted pendulum mechanism or a negative stiffness mechanism using apermanent magnet described in PTL 2 or 3. However, the stiffnesscharacteristics exhibited by such negative stiffness mechanisms arenonlinear such that the stiffness value (i.e., modulus of elasticity) isnot constant with respect to changes in displacement of a structure butthe stiffness value increases along with displacement.

When an inverted pendulum mechanism or a negative stiffness mechanismusing a permanent magnet is used, there is a possibility that as adisplacement of the structure 1 increases, the negative stiffness valuebecomes excessively large and may cause unstable behavior. Herein, “thenegative stiffness value becomes large” means that the absolute value ofthe negative stiffness value becomes large. Unstable behavior haspractical problems. Specifically, as the negative stiffness mechanismhas nonlinear stiffness characteristics, if unstable behavior occurs inthe conventional vibration damping device, a displacement of thestructure 1 at the position where the vibration damping device isdisposed would be fixed at the maximum position of the range of motionof the vibration damping device. This is because a force of the negativestiffness becomes greater than a force with which the structure 1attempts to return to the equilibrium position. When the structure 1 isfixed at the maximum position of the range of motion of the vibrationdamping device, the displacement amplification effect cannot beobtained, with the result that the vibration damping effect of thenegative stiffness cannot be exhibited at all.

To prevent such unstable behavior due to an increase in the negativestiffness value, it may be effective to set the negative stiffness valueto a small value in advance. However, with a small negative stiffnessvalue, the amount of amplification of the displacement of the structure1 also becomes small. Consequently, the vibration damping effect becomessmaller or an improvement in the vibration damping effect of the damperbecomes smaller. Further, even when the negative stiffness mechanism hasa small negative stiffness value, it has nonlinear characteristicsregarding an increase in the negative stiffness value. Thus, thephenomenon of the unstable behavior cannot be solved fundamentally.

FIG. 4 is a view illustrating an example of a displacement amplifier 7provided to the structure of the vibration damping device 100 of thepresent embodiment. The displacement amplifier 7 is a device thatamplifies a displacement due to vibration of the structure 1. Thedisplacement amplifier 7 amplifies a displacement of the structure 1using negative stiffness or negative inertia, for example. In thepresent embodiment, the displacement amplifier 7 amplifies adisplacement of the structure 1 without requiring an external energyinput. That is, the displacement amplifier 7 is a passive device. Thedisplacement amplifier 7 is a negative stiffness portion 71, forexample. The negative stiffness portion 71 is connected via the fixedplane 2 c to a position away from the fixed plane 2 b by the distance 5a at which the damper 4 of FIG. 3(a) is disposed. The negative stiffnessportion 71 is arranged so that the structure 1 has a natural length whenit stands still.

Herein, the state in which the structure 1 stands still means a state inwhich there is no displacement of the structure 1 in the directionperpendicular to the longitudinal direction thereof, which means thatthere is no vibration, that is, there is no external force other thangravity acting on the structure 1. At this time, the structure 1 is inthe equilibrium position. The negative stiffness portion 71 hascharacteristics opposite to the characteristics of common positivestiffness that represent the degree of difficulty of deformation inresponse to an applied force. While a spring having positive stiffness,for example, applies an elastic force in the direction opposite to thereceived displacement, the negative stiffness portion 71 applies anelastic force in the same direction as the received displacement.

As the negative stiffness portion 71, an inverted pendulum mechanism ora mechanism using a permanent magnet can be used. The inverted pendulummechanism is a pendulum mechanism having the center of gravity at aposition higher than a pivot. The pivot is fixed to the fixationportion, and a weight is connected to a vertically upward position ofthe structure 1 in the stand-still state. Then, when the structure isdisplaced in the transverse direction, the weight is tilted, andfurther, a force that tends to cause the structure to fall due togravity is generated. The force that tends to cause the structure tofall can be used as the negative stiffness force. However, the negativestiffness provided by the inverted pendulum is not linear. Thus, anegative stiffness force becomes greater as the displacement increases.

Meanwhile, regarding the mechanism using a permanent magnet, aferromagnetic material, such as iron, is used for the structure 1 or amember provided on the structure 1 at a position facing the displacementamplifier 7, and a permanent magnet is provided at a position away fromthe structure 1 in the stand-still state. Since there is a distancebetween the structure 1 in the stand-still state and the permanentmagnet, a magnetic force acting between them is small. However, when thestructure 1 is displaced and approaches the permanent magnet, themagnetic force attracting them to each other increases and then becomesthe negative stiffness force. However, since the magnetic force followsthe Coulomb's law and thus is inversely proportional to the square ofthe distance between the structure 1 and the permanent magnet, thenegative stiffness is nonlinear unless a special mechanism is provided.Naturally, when the structure 1 and the permanent magnet have come intocontact with each other and the distance between them has become zero,the negative stiffness force will not increase any further even if thedisplacement of the structure 1 increases.

The negative stiffness portion 71 increases a displacement of thestructure 1 a at a position where the negative stiffness portion 71 isprovided at the distance 5 a from the fixed plane 2 b. This isillustrated in FIG. 4. In FIG. 4, if the structure 1 is displaced like astructure 1 a indicated by the dotted line, the negative stiffnessportion 71 contracts by exerting a force in the same direction as thedisplacement. With this force, the structure deforms like the spatialwaveform of a structure 1 b indicated by the solid line and thus can beshaped.

In this manner, even when the displacement amplifier is provided at aposition not corresponding to the antinode of the vibration of thestructure 1, it is possible to change the spatial waveform of thevibration of the structure 1 a, that is, the vibration mode so that theantinode of the vibration of the structure 1 approaches the damper 4.Therefore, even when the damper 4 is provided at the distance 5 a (whichis less than half the length of the structure 1) from the fixed plane 2b as illustrated in FIG. 3(a), it is possible to increase the vibrationdamping effect of the damper 4 by providing the damper 4 with thenegative stiffness portion 71.

FIG. 5 is a graph illustrating an unstable phenomenon due to negativestiffness of the vibration damping device 100 of the present embodiment.In the figure, the ordinate axis indicates the negative stiffness force[N], and the abscissa axis indicates the displacement [m] of thenegative stiffness portion 71. The solid line a and the dashed line b inthe graph indicate the characteristics representing the relationshipbetween the displacement and negative stiffness force, and the slope ofeach line corresponds to the negative stiffness value.

The displacement amplifier 7 exhibits a negative stiffness force with aconstant slope as indicated by the solid line a, and should, when thestructure 1 is displaced like the structure 1 a, exert a force in thedisplacement direction that has an absolute value less than that of therestoring force generated in the direction to return to the structure 1in the stand-still state. In FIG. 5, a region c indicated in gray is aregion where the absolute value of a force generated by the displacementamplifier 7 based on negative stiffness is greater than that of therestoring force of the structure, and thus is an unstable region. In theunstable region c, vibration mode shaping by means of negative stiffnessdoes not function effectively, and the vibration damping effect of thedamper cannot be obtained.

To exert a force smaller than the force in the unstable region, it isnecessary to set the negative stiffness value of the displacementamplifier 7 to a value smaller than the slope of the solid line a.However, when an inverted pendulum mechanism or a permanent magnet isused as a machine having negative stiffness characteristics, thegenerated negative stiffness force inevitably becomes a nonlinear forcewhose slope increases along with displacement in principle as indicatedby the dotted line b. That is, provided that the intersection betweenthe solid line a, which represents linear negative stiffness as thestability limit, and the dotted line b, which represents a nonlinearnegative stiffness force of the actual negative stiffness portion 71, isindicated by an intersection d, when a displacement greater than thedisplacement x1 of the negative stiffness portion 71 at the intersectiond occurs, the operation of the vibration damping device 100 having thedisplacement amplifier 7 with such negative stiffness characteristicsbecomes unstable.

FIG. 6 is a graph illustrating the concept of preventing unstableoperation of the vibration damping device 100 due to the nonlinearstiffness characteristics of the negative stiffness portion 71, which isthe displacement amplifier 7, against vibration of the structure 1 ofthe present embodiment. Usually, in order for the vibration dampingdevice 100 to accommodate a larger vibration amplitude (i.e., excitationamplitude) of the structure 1, it is desired to expand the range ofdisplacement of the displacement amplifier 7 in which the displacementamplifier 7 can function stably. In FIG. 6, the ordinate axis indicatesthe negative stiffness force, and the abscissa axis indicates thedisplacement of the negative stiffness portion 71 as in FIG. 5. Thesolid line a in the graph indicates the stability limit at which theabsolute value of a force generated by the displacement amplifier 7using negative stiffness is equal to that of the restoring force of thestructure, and the dashed line b and the dotted line e indicate negativestiffness characteristic curves representing the relationship betweenthe displacement and negative stiffness force of the negative stiffnessportion 71.

As indicated by the dotted line e in FIG. 6, designing the negativestiffness portion 71 such that its negative stiffness force becomesweaker in comparison with the solid line a will allow the intersection dbetween the solid line a indicating the stability limit and thecharacteristic curve b of the negative stiffness portion 71 to move tothe intersection f between the solid line a and the characteristic curvee of the negative stiffness portion 71. Then, the intersection betweenthe solid line a indicating the stability limit and the characteristiccurve of the negative stiffness portion 71 moves in the direction inwhich the displacement is greater. Thus, the stable operation range ofthe vibration damping device 100 can be expanded up to a greaterdisplacement x2.

However, there is a problem in that the negative stiffness value (i.e.,the slope of each of the dashed line and the dotted line in the graph)when the displacement is around zero is small, which makes it difficultto sufficiently increase the displacement of the structure 1 with thedisplacement amplifier 7. To solve such a problem, there is a need for ameans capable of preventing unstable operation of the vibration dampingdevice without decreasing the negative stiffness value when thedisplacement is around zero.

FIG. 7 are views each illustrating the vibration damping device 100including a displacement amplifier and limiting members for controllingthe displacement amplification performed by the displacement amplifieraccording to the present embodiment. The limiting members are means forpreventing unstable operation of the vibration damping device 100. InFIG. 7(a), the negative stiffness portion 71, which is the displacementamplifier, is fixed at one end to the fixed plane 2 c and is connectedat the other end to a coupling portion 9 that is coupled to thestructure 1. Herein, the coupling portion 9 is connected to thestructure 1 so as to be capable of transmitting a force thereto. Thecoupling portion 9 may transmit a force to the structure 1 withoutcontact. The limiting members 8 are bar-like members provided on thefixed plane 2 c and protruding toward the structure 1 by a predeterminedlength. As the amplitude of the vibration force 3 increases, theamplitude of the structure 1 also increases, and when the amplitude ofthe structure 1 has increased than that in the state of the structure 1b, the structure 1 is further displaced by the displacement amplifier 7so that the coupling portion 9 becomes further closer to the fixed plane2 c.

Then, the structure 1 is displaced until the coupling portion 9 providedat the other end of the negative stiffness portion 71 collides with orcomes into contact with the limiting members 8 provided on the fixedplane 2 c. FIG. 7(b) illustrates a state in which the coupling portion 9contacts the limiting members 8. The structure 1 is deformed (displaced)up to the state of a structure 1 c illustrated in the figure. As for thestructure 1 c in the figure, the limiting members 8 provided on thefixed plane 2 c collides with or comes into contact with the couplingportion 9 provided at the other end of the negative stiffness portion71, thus the displacement amplification of the negative stiffnessportion 71 becomes limited.

Herein, the predetermined length of each limiting member 8 is the lengththat allows the limiting member 8 and the coupling portion 9 to be incontact with each other in the state in which the displacement of thenegative stiffness portion 71 does not exceed the displacement x1 at theintersection d between the stability limit line a, at which the absolutevalue of a force generated by the displacement amplifier 7 usingnegative stiffness is equal to that of the restoring force of thestructure 1, and the negative stiffness characteristic curve b of thenegative stiffness portion 71 in the graphs of FIGS. 5 and 6.

Setting the length of each limiting member 8 in the aforementionedmanner allows the vibration damping device 100 to operate stably withoutthe negative stiffness portion 71, which is the displacement amplifier7, entering the unstable region c in FIGS. 5 and 6. In addition,providing the limiting members 8 can prevent unstable operation of thenegative stiffness portion 71. Thus, it is not necessary to set thenegative stiffness value of the negative stiffness portion 71, which isthe displacement amplifier 7, low for a displacement of around zero.Therefore, both the vibration damping effect and stability of thenegative stiffness portion 71 can be provided.

Further, the limiting members 8 can also control the displacementamplifier 7 such that a force generated by the displacement amplifier 7does not exceed a force generated due to the equivalent stiffness in thedisplacement direction of the structure between the coupled position ofthe structure 1 and the fixed plane and the coupled position where thedisplacement amplifier 7 amplifies the displacement. A displacement ofthe structure 1 that occurs when a force generated by the displacementamplifier 7 exceeds a force generated due to the equivalent stiffness inthe displacement direction of the structure between the coupled positionof the structure 1 and the fixed plane and the coupled position wherethe displacement amplifier 7 amplifies the displacement is an example ofa first displacement. Herein, the first displacement is the displacementof the structure 1 by which the structure 1 is not allowed to return tothe equilibrium position of the vibration with the displacementamplifier 7. Accordingly, the limiting members 8 prevent unstablevibration of the structure 1.

FIG. 8 is a view illustrating the configuration of the vibration dampingdevice 100 provided with the negative stiffness portion 71 as thedisplacement amplifier 7 and a damper as a vibration damping meansagainst vibration of the structure 1 of the present embodiment. In FIG.8, the damper 4 is connected at one end to the coupling portion 9, whichis provided so as to be coupled to the structure 1 at a position awayfrom the fixed plane 2 b by the distance 5 a that is less than half thelength of the structure 1, together with the negative stiffness portion71, as in FIG. 7, and is connected at the other end to the fixed plane 2c together with the negative stiffness portion 71. Both the ends of thedamper 4 are connected to the coupling portion 9 and the fixed plane 2c, respectively, so as to allow a vibration damping action to actbetween them.

It has been described with reference to FIG. 3(a) that when the damper 4is provided on the fixed plane 2 c near the fixed portion of thestructure 1, the obtained vibration damping effect is small because thedisplacement of the structure 1 is small. However, even when the damper4 is provided at a similar position (i.e., the coupling portion 9 or thefixed plane 2 c), the displacement amplifier 7 illustrated in FIG. 7 canincrease the displacement of the structure 1 at the position where thevibration damping device 100 including the damper 4 is disposed. Thus,the vibration damping effect of the damper 4 is maximized.

Although FIG. 8 illustrates an example in which the damper 4 isconnected to the coupling portion 9, which is coupled to the structure1, together with the displacement amplifier, the damper 4 may beconnected to the structure 1 at a position adjacent the structure 1,separately from and in parallel with the displacement amplifier 7 (i.e.,the negative stiffness portion 71). This is because as long as thedamper 4 is located near the position where the displacement amplifieris connected to the structure 1, the effect of increasing thedisplacement of the structure 1 is obtained, and the vibration dampingeffect of the damper 4 improves. Further, when the displacementamplifier and the damper 4 are separately connected to the structure 1,the effect of preventing the structure of the vibration damping device100, such as the coupling portion 9, from becoming complex is alsoexpected.

FIG. 9 are views illustrating an example of other limiting membersaccording to the present embodiment. FIG. 9(a) is a conceptual viewillustrating the configuration of the vibration damping device 100including other limiting members. FIG. 9(b) is a graph illustrating theeffect of the configuration of FIG. 9(a).

In FIG. 9(a), the configuration of the vibration damping device 100including the fixed plane 2 c, the negative stiffness portion 71, thecoupling portion 9, and the damper 4 is the same as that in FIG. 8, butthe configuration of each limiting member 8 is different. In FIG. 9(a),each limiting member 8 is the same as that illustrated in FIG. 8 inhaving a predetermined length, but is different in having a positivestiffness portion 10 with positive stiffness. Upon receivingdisplacement, the positive stiffness portion 10 generates a repulsiveforce in the direction opposite to the displacement. With the positivestiffness portion 10 provided, each limiting member 8 is displaced inthe direction in which its length becomes shorter when the couplingportion 9 collides with the limiting member 8, and thus provides areaction force to the coupling portion 9 and eventually the structure 1.

In FIG. 8, the length of each limiting member 8 does not change.Therefore, when the coupling portion 9 collides with each limitingmember 8, neither the negative stiffness portion 71 nor the structure 1is allowed to be displaced. In contrast, in the configuration of FIG.9(a), each limiting member 8 is displaced in the direction in which thelimiting member 8 contracts after the coupling portion 9 has collidedwith the limiting member, so that the negative stiffness portion 71continues to be displaced. However, when each limiting member 8contracts, the positive stiffness portion 10 exerts a reaction force.The direction of the reaction force exerted by the positive stiffnessportion 10 is opposite to the direction of the negative stiffness forceexerted by the negative stiffness portion 71, and thus can weaken thenegative stiffness force of the negative stiffness portion 71 that hasbecome excessively large.

In the configuration of FIG. 8, the negative stiffness portion 71 isconfigured such that it is not displaced more than or equal to adisplacement to a position immediately before the safety boundary sothat the negative stiffness portion 71 will not enter the unstableregion. In contrast, in the configuration of FIG. 9(a), the negativestiffness portion 71 is greatly displaced more than the displacement x1at the safety boundary in the example of FIG. 8, but an offset force isgenerated to prevent an excessively large negative stiffness force. Thiscan increase the range of displacement within the safety region of thenegative stiffness portion 71, which is the displacement amplifier.

FIG. 9(b) is a graph illustrating the effect of the configuration ofFIG. 9(a). In the figure, the ordinate axis indicates the negativestiffness force, and the abscissa axis indicates the displacement of thenegative stiffness portion 71 as in FIG. 5. The solid line a in thegraph indicates the stability limit at which the absolute value of aforce generated by the displacement amplifier 7 using negative stiffnessis equal to that of the restoring force of the structure, and the dashedline b indicates a negative stiffness characteristic curve representingthe relationship between the displacement and negative stiffness forceof the negative stiffness portion 71. The alternate long and short dashline g indicates a force generated by the positive stiffness portion 10attached to each limiting member 8, which is a restoring force exertedso that the displacement returns to the zero position. In this graph,the negative stiffness force corresponds to the positive direction ofthe ordinate axis. Thus, the value of a force generated by the positivestiffness portion 10 has a negative value.

In FIG. 9(b), the coupling portion 9 is configured to come into contactwith the limiting members 8 when the coupling portion 9 (or the negativestiffness portion 71) has been displaced by 0.6 [m]. The resultant forceof the limiting members 8 and the negative stiffness portion 71 is theforce allowed to act on the structure 1 b by the displacement amplifier7, and is represented by the dotted line h in FIG. 9(b). The resultantforce of the limiting members 8 and the negative stiffness portion 71has characteristics of the curve b until the coupling portion 9 comesinto contact with the limiting members 8, and has the characteristics ofthe curve h after it has contacted the limiting members 8.

When the device displacement is smaller than the displacement x3 at theintersection between the safety limit curve a and the resultant forcecurve h of the limiting members 8 and the negative stiffness portion 71,the resultant force of the limiting members 8 and the negative stiffnessportion 71 is less than or equal to the safety limit curve a.Accordingly, the stable region of the vibration damping device 100 canbe expanded from x1 to x3, which corresponds to a displacement at theintersection between the safety limit curve a and the resultant forcecurve h, without the negative stiffness value decreased at a devicedisplacement of around zero.

FIG. 10 are views in which the vibration damping device 100 of thepresent embodiment is applied to a structure having no fixed plane ateither end thereof. FIG. 10(a) illustrates an example in which thevibration damping device 100 is applied to a structure 1 d that isconnected at one end to the fixed plane 2 a and is free at the otherend. In the figure, the structure 1 d to which the vibration dampingdevice 100 is applied has a smaller amplitude at a position closer tothe fixed plane 2 a, but the vibration damping device 100 can be moreeasily provided at a position close to the fixed plane 2 a. Herein, thefixed plane 2 c is provided at a position close to the fixed plane 2 a,and the aforementioned vibration damping device 100 is provided betweenthe fixed plane 2 c and the structure 1 d. Even when the vibrationdamping device 100 is provided at a position where a displacement of thestructure 1 d is small, the displacement is increased by the negativestiffness portion 71 and the vibration mode is changed, and also, thelimiting members 8 prevent excessive amplification of the displacement.Thus, a stable damping effect can be provided.

As illustrated in the figure, the damper 4 may also be provided on thecoupling portion 9, which is coupled to the structure 1 d, together withthe negative stiffness portion 71. Such a configuration can increase thevibration damping effect of the damper 4. Further, each limiting member8 may be configured to include the positive stiffness portion 10 toexpand the range of displacement in the stable region. Although thefigure illustrates a configuration in which the fixed plane 2 a isprovided in a vertically upward position and the structure 1 d hangstherefrom, it is also possible to provide a configuration in which thefixed plane is provided in a vertically downward position and thestructure 1 d is provided thereon in an upright position.

FIG. 10(b) illustrates an example in which the vibration damping device100 is applied to a structure 1 e whose both ends are free. In thisexample, the center of the structure 1 e is fixed. The vibration dampingdevice 100 is arranged at a position close to the fixed portion of thestructure 1 e. A displacement of the structure 1 e in FIG. 10(b) issmall at its center portion. Therefore, providing the damper 4 at thecenter portion would not be very effective. However, even when thedamper 4 is provided at a similar position (i.e., the coupling portion 9or the fixed plane 2 c), the displacement amplifier 7 can increase thedisplacement of the structure 1 at the position where the vibrationdamping device 100 including the damper 4 is disposed. Thus, thevibration damping effect of the damper 4 is maximized.

In the figure, the aforementioned vibration damping device 100 isprovided between the fixed plane 2 c and the structure 1 d. Even whenthe vibration damping device 100 is provided at a position where adisplacement of the structure 1 e is small, the displacement isincreased by the negative stiffness portion 71 and the vibration mode ischanged, and also, the limiting members 8 prevent excessiveamplification of the displacement. Thus, a stable damping effect can beprovided.

As in FIG. 10(a), the damper 4 may be provided on the coupling portion9, which is coupled to the structure 1 d, together with the negativestiffness portion 71. Further, even when each limiting member 8 isconfigured to include the positive stiffness portion 10, the same effectas that described above can be obtained.

FIG. 11 are views each illustrating an example in which the vibrationdamping device 100 according to the present embodiment is not connectedto anything other than the structure. That is, the structure in FIG. 11does not have the fixed plane 2 c, but instead, the vibration dampingdevice 100 has a coupling portion 9 a that is coupled to the structure 1d at a second position away from a first position at which the couplingportion 9 is coupled to the structure 1 d. In addition, the negativestiffness portion 71, which is a displacement amplifier, is providedbetween the first coupling portion 9 coupled to the structure 1 d at thefirst position and the second coupling portion 9 a coupled to thestructure 1 d at the second position.

The vibration damping device 100 is configured such that the coupledpositions (i.e., the first position and the second position) of thefirst coupling portion 9 and the second coupling portion 9 a are awayfrom each other. Thus, when the structure 1 vibrates and deforms into awave shape, a displacement of the first coupling portion 9 in thedirection perpendicular to the longitudinal direction of the structure 1d differs from that of the second coupling portion 9 a. Such adifference in displacement is increased by the negative stiffnessportion 71, which is the displacement amplifier, and the vibration modeof the structure 1 d is changed. Thus, the damping effect of the damper4 can be increased.

In addition, in FIG. 11, each limiting member 8 is provided at the firstcoupling portion 9 or the second coupling portion, and prevents thenegative stiffness portion 71 from being displaced by a degree greaterthan or equal to a predetermined displacement, or each positivestiffness portion 10 exerts a force in the direction opposite to anegative stiffness force exerted by the negative stiffness portion 71,thereby preventing the negative stiffness force from becomingexcessively large.

In the vibration damping device 100, the coupled position of thestructure 1 and the displacement amplifier 7 (or the coupling portion 9)may be arranged at a position closer to the node than to the antinode ofthe vibration of the structure 1. Herein, the distance between thecoupled position and the node of the vibration of the structure 1 isshorter than the distance between the coupled position and the antinodeof the vibration of the structure 1. In addition, the distance betweenthe coupled position and the node of the vibration of the structure 1 isgreater than zero. Providing the coupled position at a position closerto the node than to the antinode of the vibration of the structure (whenit vibrates at its natural frequency) can change the vibration mode moreeasily, which can increase the vibration damping effect. This is becauserather than providing the displacement amplifier 7 at a position closerto the antinode of the vibration to further increase the displacement,providing the displacement amplifier 7 at a position closer to the nodeof the vibration at which the displacement is small will allow anotherantinode of the vibration to be generated and thus will change thevibration mode to a different vibration mode. Then, the frequency of thenew vibration mode (after the change) typically becomes low, and it isthus expected that the frequency be away from the previous naturalfrequency (before the change) and the amplitude be small. By changingthe natural frequency in this manner, the vibration damping device 100is expected to avoid resonance of the structure 1 even when aconfiguration without the damper is employed.

According to the present embodiment, the vibration damping device 100includes the displacement amplifier 7 that is arranged along anyposition in the longitudinal direction of the structure and thatamplifies a displacement of the structure, and the limiting members 8that control the displacement amplification performed by thedisplacement amplifier 7 such that the displacement of the structureamplified by the displacement amplifier 7 will not become greater than apreset displacement. Herein, the preset displacement is the firstdisplacement of the structure 1 by which the structure 1 is not allowedto return to the equilibrium position of the vibration. Accordingly, thevibration damping device 100 can stably increase a displacement due tovibration of the structure at the position where the displacementamplifier 7 is provided, and can thus increase the vibration dampingeffect.

The displacement amplifier 7 may be arranged at a position closer to thenode than to the antinode of the vibration of the structure. Herein, thedistance between the position of the displacement amplifier 7 and thenode of the vibration of the structure 1 is shorter than the distancebetween the coupled position and the antinode of the vibration of thestructure 1. Further, the distance between the position of thedisplacement amplifier 7 and the node of the vibration of the structure1 is greater than zero. Then, it follows that the displacement amplifier7 is arranged at a position closer to the node than to the antinode ofthe waveform of the vibration of the structure in the natural vibrationmode. Thus, the waveform of the vibration of the structure, and hencethe vibration mode can be changed.

The displacement amplifier 7 is configured with a simple structure of anegative stiffness member, such as a permanent magnet or an invertedpendulum. Therefore, vibration can be controlled without a power supplyand without requiring a reduction in weight, improvement in durability,or control.

Each limiting member is configured with an elastic body having positivestiffness. Therefore, when a displacement of the structure has reached apreset displacement, the elastic body is displaced in the direction inwhich it becomes shorter, thereby applying a force to the structure inthe direction opposite to the displacement of the structure. Then, sincethe direction of the force exerted by the elastic body is opposite tothe direction of a negative stiffness force exerted by the displacementamplifier 7, the elastic body can suppress an excessive negativestiffness force of the displacement amplifier 7 and thus can avoidunstable operation thereof.

In addition, each limiting member is configured to control thedisplacement amplifier 7 such that a force generated by the displacementamplifier 7 does not exceed a force generated due to the equivalentstiffness in the displacement direction of the structure between thefixed position of the structure and the coupled position where thedisplacement amplifier amplifies the displacement. Therefore, thedisplacement amplifier 7 can be prevented from becoming unstable whileexerting a vibration damping effect.

The preset first displacement for each limiting member is a displacementat which a force exerted by the displacement amplifier 7 exceeds a forcegenerated due to the equivalent stiffness in the displacement directionof the structure between the fixed position of the structure and thecoupled position where the displacement amplifier 7 amplifies thedisplacement. Therefore, the displacement amplifier 7 can be preventedfrom becoming unstable while exerting a vibration damping effect.

The displacement amplifier 7 is configured to apply the components of aforce in the vibration (displacement) direction of the structure andthus in the displacement direction thereof. Therefore, the displacementamplifier 7 can exhibit a vibration damping effect.

The vibration damping device 100 also includes a vibration damper thatreduces vibration of the structure. Therefore, vibration energy can beefficiently dissipated by the displacement amplifier 7 and the limitingmembers, and thus a high vibration damping effect can be obtained.

Examples of a structure that is fixed at both ends to fixed planes asillustrated in FIG. 1 include an elevator rope, a timing belt, a maincable of a suspension bridge, and a wire of an electric dischargemachine. In addition, examples of a structure that is fixed at one endto a fixed plane and is free at the other end as illustrated in FIG.10(a) include a wire rope of a crane and an antenna. Further, examplesof a structure that is free at both ends as illustrated in FIG. 10(b)include a structure having no fixed planes, such as a tetheredsatellite. Applying the configuration of the present embodiment to anyof such examples can stably increase the vibration damping effect.

Embodiment 1 has described control of transverse vibration that isperpendicular to the longitudinal direction of a structure. However, itis also possible to apply the configuration of the present embodiment tocontrol of longitudinal vibration that is parallel with the longitudinaldirection of a structure by changing the direction of the displacementamplifier 7 and the vibration damping effect as with the case ofcontrolling transverse vibration so that the vibration damping effectcan be stably increased.

Embodiment 2

The present embodiment will describe an embodiment in which a vibrationcontrol target of the vibration damping device 100 is an elevator rope,and the concept of the vibration damping device of Embodiment 1 isapplied thereto.

FIG. 12 is a schematic view illustrating the configuration of anelevator apparatus according to the present embodiment. FIG. 12illustrates the x-axis, y-axis, and z-axis of the 3-axis orthogonalcoordinate system. In FIG. 12, the vertically downward direction is thepositive direction of the x-axis. FIG. 12 schematically illustrates theelevator apparatus in a state where there is no building sway and thusno vibration is generated. Hereinafter, the building will not bedescribed in detail, but portions related to the elevator apparatus willbe mainly described. In addition, the support portion for each part, acontrol unit, and the like are omitted.

In FIG. 12, a machine room 29 is provided in the upper portion of anelevator apparatus 11, and a traction machine 12, a deflector sheave 13,and a governor 19 are provided in the machine room 29. A car 14 forcarrying passengers is connected to one end of a main rope 16, and theother end of the main rope 16 is connected to a counterweight 15 via thetraction machine 12 and the deflector sheave 13.

Upon rotation of the traction machine 12, the car 14 connected to themain rope 16 is raised or lowered in the vertical direction (i.e.,x-axis direction in FIG. 12) due to a frictional force between a sheaveprovided on the shaft of the traction machine 12 and the main rope 16.As the counterweight 15 is connected to the other end of the main rope16 on the side opposite to the one end thereof connected to the car 14,the dead load of the car 14 is offset and the driving force of thetraction machine 12 is reduced.

As the car 14 is raised or lowered, the length of the main rope 16 onthe side of the car 14 and that on the side of the counterweight 15across the traction machine 12 will change. Then, since the main rope 16also has its dead load per unit length, the mass of the traction machine12 on the side of the car 14 and that on the side of the counterweight15 become unbalanced. To compensate for such unbalanced mass, acompensating rope 17, which is connected at one end to the bottom sideof the car 14 and is connected at the other end to the counterweight 15,is provided via compensating sheaves 18.

Further, to identify the raised or lowered position of the car 14 in thevertical direction (i.e., x-axis direction), a governor rope 20 coupledto the car 14, the governor 19 on which the governor rope 20 is wound,and a governor tension sheave 21 located on the side opposite to thegovernor 19 are provided so that they move as the car 14 is raised orlowered. The governor rope 20 is rigidly coupled to the car 14 and movesas the car 14 is raised or lowered. Thus, the moving quantity of thegovernor rope 20 is measured by an encoder provided on the governor 19.In addition, the car 14 is provided with a traveling cable 22 fortransmitting power and information signals. Herein, the structure 1 thatis a vibration control target of Embodiment 2 is an elevator rope. Theelevator rope is a cord-like structure of the elevator apparatus 11.Examples of the elevator rope include the main rope 16, the compensatingrope 17, the governor rope 20, and the traveling cable 22. The elevatorrope includes a wire rope and a belt rope. The elevator rope is made ofa ferromagnetic material, for example. Alternatively, the elevator ropemay have a ferromagnetic material on its surface so as to have aferromagnetic property, for example.

FIG. 13 is a view illustrating the time when building sway 23 occurs inthe elevator apparatus illustrated in FIG. 12 due to turbulence, such asearthquakes or winds, for example. When the building sway 23 occurs, thetraction machine 12 and the governor 19 fixed to the building also swayin a similar manner, so that the main rope 16, the compensating rope 17,the governor rope 20, and the traveling cable 22, which are the ropes(i.e., elevator ropes) of the elevator apparatus, are vibrated. At thistime, if the vibration frequency of the building sway 23 coincides withthe natural frequency of any of the elevator ropes, a resonancephenomenon occurs, which amplifies the sway. FIG. 13 exemplarilyillustrates a state where the natural frequency of the main rope 16 acoincides with the vibration frequency of the building sway, and thus aresonance phenomenon occurs on the main rope 16.

FIG. 14 is a view illustrating an example of the vibration dampingdevice 100 that controls vibration of the main rope 16 of the elevatorapparatus according to the present embodiment. The range of the mainrope whose vibration is controlled by the vibration damping device 100is between an end B1 of the main rope close to the traction machine anda coupled portion B2 of the car and the main rope. Hereinafter, thedistance between the end B1 of the rope and the coupled portion B2 ofthe car and the main rope shall be referred to as the length of the mainrope unless otherwise stated. FIG. 14 illustrates an example in whichthe vibration damping device 100 for the elevator apparatus is disposedon a machine room floor 28, and the displacement amplifier 7 includespermanent magnets. The machine room floor 28 has a rope duct 28 a. Therope duct 28 a is an opening leading to the hoistway from the machineroom 29. The main rope 16 a is passed through the rope duct 28 a.

Although FIG. 14 illustrates an example in which the vibration dampingdevice 100 for the elevator apparatus is disposed on the machine roomfloor 28, this is only exemplary and the position of the vibrationdamping device 100 is not limited thereto. The vibration damping device100 may be disposed at any position within the range of the end B1 tothe coupled portion B2 of the rope in a state where the car 14 isstopped at the top floor.

In the present embodiment, the displacement amplifier 7 is a passivedevice. In this example, the negative stiffness portion 71 as thedisplacement amplifier 7 of the vibration damping device 100 ofEmbodiment 2 includes a pair of magnet units 54. Each of the pair ofmagnet units 54 includes permanent magnets 24 (24 a and 24 b) and a yoke25. The permanent magnets 24 (24 a and 24 b) are provided so as to faceeach other at symmetrical positions across the main rope 16 (indicatedby the dotted line in the figure). The yoke 25 is arranged along adirection parallel with the main rope 16. The magnetic poles of thepermanent magnet 24 a are directed toward the upper end of the yoke 25from the direction of the main rope 16. The magnetic poles of thepermanent magnet 24 b are opposite to those of the permanent magnet 24 aand are directed toward the lower end of the yoke 25 from the directionof the main rope 16. The magnetic poles of the magnet unit 54 are, forexample, the magnetic poles of the permanent magnets 24 that do not facethe yoke 25. The pair of magnet units are arranged with their samemagnetic poles facing each other. The negative stiffness portion 71,which is the displacement amplifier 7 of Embodiment 2, includes thepermanent magnets 24 a and 24 b. The limiting members include limitingmembers 8 a formed of a non-magnetic material. An attraction forceacting on the main rope 16 due to the magnetic forces of the permanentmagnets 24 (24 a and 24 b) increases in inverse proportion to thedistance between the permanent magnets 24 (24 a and 24 b) and the mainrope 16 a. When the main rope 16 a is displaced from the stand-stillstate, a force attracted in the displacement direction acts on the mainrope 16 a utilizing the aforementioned property, which further increasesthe displacement of the main rope 16 a. In this manner, the permanentmagnets 24 generate a negative stiffness force and thus exhibit thefunction of the displacement amplifier.

The pair of magnet units 54 may be provided at different heights acrossthe main rope 16.

The negative stiffness portion 71 as the displacement amplifier 7 of thevibration damping device 100 of Embodiment 2 may include at least onemagnet unit 54. In addition, more than one magnet unit 54 may bearranged along the longitudinal direction of the main rope 16.

Since the attraction force of the permanent magnets 24 is inverselyproportional to the distance between the permanent magnets 24 and themain rope 16 a, the attraction force has nonlinear characteristics withrespect to the displacement of the main rope 16 a. Utilizing thegeometric symmetry of the device arrangement can, when a nonlinearelement is series-expanded, cancel even-ordered terms. Thus, thenegative stiffness portion 71 is configured to have the minimumnonlinearity.

In FIG. 14, the yoke 25 arranged on the side faces of the permanentmagnets, a coil 26 wound on the yoke 25, and an electric resistor 27electrically connected to the coil 26 are provided. The yoke 25, thecoil 26, and the electric resistor 27 implement the characteristics of adamper as a vibration damping portion.

This is because as the displacement of the main rope 16 a changes, themagnetic flux of each permanent magnet changes, and the magnetic fluxpassing through the yoke 25 also changes. When the magnetic flux passingthrough the yoke 25 has changed and the magnetic flux passing throughthe coil 26 has changed, a voltage is generated in the coil 26 due to anelectromagnetic induction phenomenon. As a voltage is generated acrossthe both ends of the coil 26, a current flows through the electricresistor 27 and the electric resistor dissipates Joule heat. This meansthat vibration energy, which is a change in the displacement of the mainrope 16 a, is eventually dissipated as Joule heat by the electricresistor 27. The amount of change in the magnetic flux passing throughthe coil 26 depends on the speed of the displacement of the main rope 16a. Consequently, the same effect as when a mechanical damper is attachedcan be obtained with the coil 26 and the electric resistor 27. Thelimiting members 8 a are non-magnetic bodies and are attached to themagnets 24 a and 24 b, respectively. The thickness of each limitingmember 8 a is set in the range that can prevent the main rope 16 frombecoming unstable due to negative stiffness. Each limiting member 8 alimits the distance between the main rope 16 a and each magnet 24 sothat the distance does not become less than the thickness of thelimiting member 8 a.

The limiting members 8 control a force exerted by the displacementamplifier 7 to be smaller than a force with which the elevator ropeattempts to return to the equilibrium position (i.e., the position inthe stand-still state) with the tension of the elevator rope. This canprevent the vibration from entering the unstable region.

The displacement amplifier 7 may be arranged at a position closer to thesheave (i.e., the traction machine or the deflector sheave) on which theelevator rope is wound than to the car 14 or the counterweight 15. Thedisplacement amplifier 7 may be arranged at a position closer to the car14 or the counterweight 15 or to the sheave on which the elevator ropeis wound than to the center position of the elevator rope. The centerposition of the elevator rope is the midpoint between the fixed positionB1 and the fixed position B2, for example. At this time, the distancebetween the position of the displacement amplifier and the car 14 or thecounterweight 15, or the sheave is shorter than the distance between thedisplacement amplifier and the center position of the elevator rope. Thedistance between the position of the displacement amplifier and the car14 or the counterweight 15, or the sheave is greater than zero.Accordingly, it becomes easier to change the vibration mode of theelevator rope to another vibration mode at a position away from theantinode of the vibration of the primary vibration mode.

The displacement amplifier 7 is formed of a negative stiffness memberthat exerts a force corresponding to a transverse displacement of theelevator rope in a direction away from the equilibrium position of theelevator rope. Accordingly, vibration of the elevator rope can beeffectively controlled.

FIG. 15 is a view of the vibration damping device 100 obtained byproviding roller-type limiting members on the vibration damping device100 of the present embodiment. The main rope 16 a moves in the x-axisdirection as the car 14 is raised or lowered. Thus, in the vibrationdamping device 100 including the limiting members 8 a as illustrated inFIG. 14, a friction force may be generated when the main rope 16 a andthe limiting members 8 a come into contact with each other, which canpromote the deterioration of the main rope 16 a.

In FIG. 15, limiting members 8 b each having a roller at its tip aredisposed as limiting devices between the vibration damping device 100and the main rope 16 a, so that the rollers at the tips of the limitingmembers 8 b first come into contact with the main rope 16 a, therebyreducing the load on the main rope 16 a in the vertical direction (i.e.,x-axis direction). Meanwhile, the limiting members 8 b can limit adisplacement of the main rope 16 a in the transverse direction (i.e.,y-axis direction) that is orthogonal to the vertical direction.

In addition, the limiting members 8 b each having a roller at its tipcan be attached to a non-magnetic fixation member 30 via the positivestiffness portions 10. Accordingly, when the negative stiffness force(i.e., attraction force) of the permanent magnets as the negativestiffness portion 71 has become excessively large as in FIG. 9 ofEmbodiment 1, the positive stiffness portions 10 can exert a force inthe direction opposite to the negative stiffness force and thus canexpand the stable range of the permanent magnets, which is the negativestiffness portion 71. Further, attaching the limiting members 8 b to thenon-magnetic fixation member 30 can reduce the influence on the functionof the damper including the permanent magnets 24, the yoke 25, the coil26, and the electric resistor 27.

Described above is an example in which a vibration damping portion(i.e., damper) is formed by providing the yoke 25, the coil 26, and theelectric resistor 27. However, even without such a damper, the naturalfrequency becomes a low frequency and resonance with the building sway23 can be avoided, thus exhibiting a vibration damping effect. That is,limiting devices each including the permanent magnet 24 as the negativestiffness portion 71 and the limiting member 8 b having a roller at itstip may be used. Alternatively, limiting devices each including thepermanent magnet 24 and the limiting member 8 b, which has a roller atits tip and includes the positive stiffness portion 10, may also beused. Accordingly, the vibration damping device 100 can be provided thatprevents the negative stiffness force of the negative stiffness portion71 from becoming excessively large and thus can prevent the negativestiffness portion 71 from becoming unstable.

Although the aforementioned vibration damping device 100 is providednear the traction machine 12 that is provided in the machine room anddisposed in a vertically upward position, the vibration damping device100 may also be provided at a position near the joined portion of thecar 14 and the main rope 16 or the joined portion of the counterweight15 and the main rope 16. This allows the vibration mode of the elevatorrope to be more easily changed to another mode at a position away fromthe antinode of the vibration of the primary vibration mode. That is, itis effective to provide the vibration damping device 100 at a positionaway from the antinode of the vibration of the primary vibration mode.

FIG. 16 is a view of the vibration damping device 100 of the presentembodiment provided in the rope duct 28 a. The vibration damping device100 includes a pair of permanent magnets 24 and a pair of limitingmembers 8 d. The permanent magnets 24 are examples of the magnet units.One of the pair of permanent magnets 24 is arranged on the inner side ofone of the pair of limiting members 8 d. The other of the pair ofpermanent magnets 24 is arranged on the inner side of the other of thepair of limiting members 8 d.

The pair of limiting members 8 d are provided in the rope duct 28 a. Thepair of limiting members 8 d are arranged at symmetrical positionsacross the main rope 16 a. For example, when the rope duct 28 a is arectangular opening, the pair of limiting members 8 d are provided onopposite sides of the rope duct 28 a. The pair of limiting members 8 dface each other across the main rope 16 a.

The pair of permanent magnets 24 are provided in the rope duct 28 atogether with the pair of limiting members 8 d. Each of the pair ofpermanent magnets 24 is arranged with its magnetic pole facing the mainrope 16 a. The magnetic pole of each of the pair of permanent magnets 24is covered with each of the pair of limiting members 8 d.

Accordingly, the vibration damping device 100 becomes compact.Therefore, the vibration damping device 100 can also be applied to anelevator apparatus in which the distance from the rope duct 28 a to thetraction machine 12 is short.

FIGS. 17 and 18 are views each illustrating an example in which thevibration damping device 100 that controls vibration of the main rope 16of the elevator according to the present embodiment is configured with alink mechanism. As illustrated in FIG. 17, the negative stiffnessportion 71 of the vibration damping device 100 has a line-symmetricstructure with respect to the main rope 16 in the stand-still state asthe axis of symmetry (as seen in the section of the xy plane in thefigures, for example), as with the vibration damping device 100illustrated in FIG. 14.

Each side of the line-symmetric negative stiffness portion 71 of thevibration damping device 100 has a toggle link mechanism 31 thatincludes a weight 31 a, a link 31 b, and a rotation pivot 31 c. Thetoggle link mechanism 31 is fixed at one end to the car 14 and is fixedat the other end to a rope restraining member 32 or at the rotationpivot. The rope restraining member 32 is coupled to one or more mainropes 16 a, and is supported by a linear guide 33 so as to be freelymovable in the horizontal direction (i.e., y-axis direction). The linearguide 33 may include a pair of rollers that contact with the main rope16 interposed therebetween.

The displacement of the rope restraining member 32 in the horizontaldirection is limited by the limiting members 8 c provided on the fixedplane. The limiting members 8 c prevent the negative stiffness forceexerted by the toggle link mechanism 31, which is the negative stiffnessportion 71, from becoming excessively large and thus prevent the togglelink mechanism 31 from becoming unstable. FIG. 16(a) is a front view ofthe vibration damping device 100 as viewed from the side in thehorizontal direction, while FIG. 17 is a top view of the vibrationdamping device 100 as viewed from a vertically upward position.

Next, the function of the configuration illustrated in FIGS. 17 and 18will be described. In FIG. 16, when the main rope 16 a is displaced, itcomes into contact with the rope restraining member 32, and thus, therope restraining member 32 is displaced. Then, the link 31 b of thetoggle link mechanism 31 on the side of the displacement directionconnected to the rope restraining member 32 is folded, while the link 31b of the toggle link mechanism 31 on the other side has an extendedshape. Each toggle link mechanism 31 is a mechanism that generates agreat force (in this case, a negative stiffness force) when it extendsdue to the inertia of the weight 31 a. The force transmitted by thetoggle link mechanism 31 to the main rope 16 a is greater when the link31 b extends than when it is folded. Therefore, compared to the forceapplied to the main rope 16 a by the toggle link mechanism 31 on theside of the displacement direction, the force applied to the main rope16 a by the toggle link mechanism 31 on the other side is greater.Accordingly, the toggle link mechanism 31 generates a negative stiffnessforce. The toggle link mechanism 31 is an example of an unstable linkmechanism that generates a negative stiffness force utilizing adisplacement of one or more links.

Consequently, it is possible to add a force in the same direction as thedisplacement direction of the main rope 16 a, that is, the negativestiffness characteristics of the displacement amplifier 7 utilizing thecharacteristics of the toggle link mechanism 31. Meanwhile, since thefriction of the linear guide 33 suffices as the viscosity of a vibrationdamping means, a hydraulic damper or the like is not separately attachedin this example. However, a damper may be attached when the friction ofthe linear guide 33 is insufficient, for example.

Next, the vibration damping principle of the vibration damping device100 for an elevator rope according to Embodiment 2 and methods ofdetermining the negative stiffness value and the viscosity value of thedamper will be described using mathematical expressions. Hereinafter, amethod of designing the vibration damping device which is applied to themain rope 16 among the elevator ropes will be described. However, thetheory can be similarly applied the vibration damping device which isapplied to other elevator ropes.

First, referring to FIG. 13, the main rope 16 a in a region where ithangs from the traction machine 12 to it is connected to the car 14 willbe described as the main rope 16. Considering vibration of the main rope16 a, both ends of the structure correspond to the end B2 of the mainrope 16 in contact with the sheave of the traction machine 12 and theend B1 of the main rope 16 connected to the car 14. Let the distancebetween the ends B1 and B2 be L. Let the end B1 of the main rope 16 bethe origin, and let the vertically downward direction be the positivedirection of the x-axis. A transverse vibration displacement of the mainrope 16 a at a position away from the origin by the distance x at thetime t is expressed as a function v(x,t). At this time, thespatio-temporal characteristics of the main rope 16 a are governed by anequation of motion represented by Expression (1).

$\begin{matrix}\left\lbrack {{Math}.\mspace{11mu} 1} \right\rbrack & \; \\{{\rho \frac{\partial^{2}{v\left( {x,t} \right)}}{\partial t^{2}}} = {{T\frac{\partial^{2}{v\left( {x,t} \right)}}{\partial x^{2}}} - {F_{cmp}{\delta \left( {x - x_{0}} \right)}}}} & (1)\end{matrix}$

Herein, p is the linear density of the main rope 16 a, F_(cmp) is aforce applied to the main rope 16 a by the vibration damping device 100,δ(·) represents the delta function, and x₀ represents the position wherethe vibration damping device 100 is disposed. T represents the tensionof the main rope 16 a, which is constant herein. The left-hand side ofExpression (1) represents the inertial force of a small point massobtained by multiplying the linear density by the acceleration of thepoint mass (i.e., second-order partial differentiation with respect tothe time of the vibration displacement function v(x,t)). This shows thatthe left-hand side is balanced with the difference between thecomponents of a force in the horizontal direction of the tension Tacting on both ends of the small point mass (i.e., second-order partialdifferentiation with respect to the position x of the vibrationdisplacement function v(x,t)). Further, the force F_(cmp) of thevibration damping device 100 is added at the position x₀. Expression (1)is known as an equation representing a wave propagation, and is called awave equation. The wave propagation speed c is represented by Expression(2).

$\begin{matrix}\left\lbrack {{Math}.\mspace{11mu} 2} \right\rbrack & \; \\{c = \sqrt{\frac{T}{\rho}}} & (2)\end{matrix}$

Expression (2) represents that the wave propagation speed c of the mainrope 16 a is the square root of the tension T of the main rope 16 adivided by the linear density p. The boundary conditions for the mainrope 16 a are represented by the following Expressions (3) and (4).

[Math. 3]

v(0,t)=v _(eXt)  (3)

[Math. 4]

v(L,t)=0  (4)

Herein V_(ext) represents the displacement of building sway. Expression(3) represents that a forced displacement V_(ext) is applied to the endB1 of the main rope 16 a due to the building sway. Meanwhile, Expression(4) represents that the displacement of the end B2 whose distance fromthe end B1 is L is zero, that is, the end B2 is fixed. The initialconditions are such that the main rope 16 stands still at t=0.

Using the aforementioned boundary conditions and the initial conditionscan determine the exact solution of the transfer function of the waveequation represented by Expression (1), which is represented by thefollowing Expression (5).

$\begin{matrix}{\mspace{79mu} \left\lbrack {{Math}.\mspace{14mu} 5} \right\rbrack} & \; \\{{V\left( {x,s} \right)} = {{\left\lbrack \frac{e^{{- \frac{s}{c}}x} - e^{{- \frac{s}{c}}{({{2L} - x})}}}{1 - e^{{- \frac{s}{c}}2L}} \right\rbrack\left\lbrack {V_{ext} - {\frac{c}{2s}\left( {e^{\frac{s}{c}x_{0}} - e^{{- \frac{s}{c}}x_{0}}} \right)\frac{1}{T} F_{cmp}}} \right\rbrack} = {\quad{\left\lbrack \frac{\sinh \frac{s}{c}\left( {L - x_{0}} \right)}{\sinh \frac{s}{c}L} \right\rbrack \left\lbrack {V_{ext} - {\frac{c}{s}*\sinh \frac{s}{c}x_{0}*\frac{1}{T}F_{cmp}}} \right\rbrack}}}} & (5)\end{matrix}$

Herein, s represents the Laplacian operator, and sinh represents thehyperbolic function.

Herein, to design the vibration damping device 100 that can beimplemented using a mechanical element that outputs the vibrationdamping force F_(cmp), approximation by means of infinite productexpansion is applied to the hyperbolic function of Expression (5). Whenthe approximation is applied, it is assumed that the position x₀ wherethe vibration damping device 100 is disposed is a position whosedistance from the end B1 is sufficiently smaller than the length L ofthe main rope 16, that is, a position close to the end B1 on the side ofthe traction machine. Based on the foregoing assumption, transferfunctions up to the transverse vibration displacement V(x₀,$) of themain rope 16 at the position where the vibration damping device isdisposed and the transverse vibration displacement V(L/2,$) of the mainrope 16 at the center position thereof are represented by the followingExpressions (6) and (7), respectively.

$\begin{matrix}{\mspace{79mu} \left\lbrack {{Math}.\mspace{14mu} 6} \right\rbrack} & \; \\{{V\left( {x_{0},s} \right)} = {{\left( \frac{L - x_{0}}{L} \right)^{3}{\frac{s^{2} + \omega_{x0}^{2}}{s^{2} + \omega_{L}^{2}}\left\lbrack {V_{ext} - {\frac{x_{0}}{T}F_{cmp}}} \right\rbrack}} = {\alpha {\frac{s^{2} + \omega_{x0}^{2}}{s^{2} + \omega_{L}^{2}}\left\lbrack {V_{ext} - {\frac{x_{0}}{T}F_{cmp}}} \right\rbrack}}}} & (6)\end{matrix}$

It should be noted that α=(L−x₀)³/L³ for simplification.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 7} \right\rbrack & \; \\{{V\left( {{L/2},s} \right)} = {\frac{1}{2}\frac{L}{\left( {L - x_{0}} \right)}\frac{\omega_{x0}^{2}}{s^{2} + \omega_{x\; 0}^{2}}{V\left( {x_{0},s} \right)}}} & (7)\end{matrix}$

Herein, ω_(L) and ω_(x0) are respectively the primary naturalfrequencies of the main rope 16 when the length of the main rope 16 is Land when it has become the distance L_(x0) from the end B1 to theposition where the vibration damping device 100 is disposed. These arerepresented by Expressions (8) and (9), respectively.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 8} \right\rbrack & \; \\{\omega_{L} = {\frac{\pi}{L}\sqrt{\frac{T}{\rho}}}} & (8) \\\left\lbrack {{Math}.\mspace{14mu} 9} \right\rbrack & \; \\{\omega_{x0} = {\frac{\pi}{L - x_{0}}\sqrt{\frac{T}{\rho}}}} & (9)\end{matrix}$

Herein, it is assumed that the force F_(cmp) output from the vibrationdamping device 100 (i.e., the negative stiffness force of the negativestiffness portion 71) is the resultant force of the stiffness and theviscous element represented by the following Expression (10).

[Math. 10]

F _(cmp)(K _(p) +D _(p) s)V(x ₀ ,s)=G( K _(p) +D _(p) s)V(x ₀ ,s)  (10)

Herein, K_(p) and D_(p) represent the stiffness value and the viscosityvalue of the displacement amplifier 7 (i.e., the negative stiffnessportion 71), respectively. In addition, K_(p) bar and D_(p) bar(notations of lines above the symbols) represent the stiffness value andthe viscosity value of the displacement amplifier 7 (i.e., the negativestiffness portion 71) normalized by the constant G, respectively. Theconstant G is given by the following value.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 11} \right\rbrack & \; \\{G = \frac{T}{x_{0}}} & (11)\end{matrix}$

Substituting Expression (10), which represents the force applied by thevibration damping device 100, into Expression (6), which represents thetransfer function, to calculate a characteristic polynomial can obtainthe following Expression (12).

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 12} \right\rbrack & \; \\{{D(s)} = {{\overset{\_}{D}}_{p}{\alpha \left( {s^{3} + {\frac{\left( {{{\overset{\_}{K}}_{p}\alpha} + 1} \right)}{{\overset{\_}{D}}_{p}\alpha}s^{2}} + \omega_{x0^{S}}^{2} + \frac{\omega_{L}^{2} + {\omega_{x0}^{2}{\overset{\_}{K}}_{p}\alpha}}{{\overset{\_}{D}}_{p}\alpha}} \right)}}} & (12)\end{matrix}$

Herein, the following constants are defined for simplification inExpression (12). Assuming that the damping ratio of the main rope 16 isset to 1 and the angular frequency is set to con by the vibrationdamping device 100, the characteristic polynomial is represented by thefollowing Expression (13).

[Math. 13]

D(s)= D _(p)α(s+ω _(n))³ =D _(p)α(s ³+3ω_(n) s ²+3ω_(n) s+ω _(n)³)  (13)

The conditions for setting the damping ratio to 1 with the vibrationdamping device 100 are as follows. Solving simultaneous equations inwhich the coefficients of Expressions (12) and (13) are compared withK_(p) bar, D_(p) bar and con as unknowns can obtain the followingExpressions (14), (15), and (16).

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 14} \right\rbrack & \; \\{{\overset{\_}{K}}_{p} = {\frac{1}{\alpha}\frac{1}{8}\left\{ {1 - {9\frac{\omega_{L}^{2}}{\omega_{x0}^{2}}}} \right\}}} & (14) \\\left\lbrack {{Math}.\mspace{14mu} 15} \right\rbrack & \; \\{{\overset{\_}{D}}_{p} = {\frac{1}{\alpha}\frac{1}{\sqrt{3}\omega_{x0}}\frac{9}{8}\left\{ {1 - \frac{\omega_{L}^{2}}{\omega_{x_{0}}^{2}}} \right\}}} & (15) \\\left\lbrack {{Math}.\mspace{14mu} 16} \right\rbrack & \; \\{\omega_{n} = \frac{\omega_{x0}}{\sqrt{3}}} & (16)\end{matrix}$

Multiplying the normalized stiffness value and viscosity valuecalculated with Expressions (14) and (15), respectively, by the constantG can obtain the actual stiffness value and viscosity value. Inaddition, referring to Expression (14), the value is negative due to thecondition that the value of ω_(L) is close to ω_(x0), and thus, it isfound that implementation of negative stiffness is indispensable forcontrolling vibration of the main rope 16.

Further, applying the negative stiffness to the vibration damping device100 will change the maximum damping ratio that can be obtained byadjusting the viscosity value (hereinafter referred to as the maximumdamping ratio). The maximum damping ratio is represented as the functionof the normalized negative stiffness value K_(p) bar and is given by thefollowing Expression (17).

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 17} \right\rbrack & \; \\{{\zeta \left( {\overset{\_}{K}}_{p} \right)} = {\frac{1}{2}\left( \sqrt{1 + \frac{\omega_{x0}^{2} - \omega_{L}^{2}}{\omega_{L}^{2} + {\alpha {\overset{\_}{K}}_{p}\omega_{x0}^{2}}} - 1} \right)}} & (17)\end{matrix}$

In particular, when the normalized negative stiffness value K_(p) bar iszero, the maximum damping ratio is equivalent to that when the vibrationdamping device 100 is constructed using only a viscous element. In thatcase, the maximum damping ratio ζ is represented by the followingExpression (18).

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 18} \right\rbrack & \; \\{{\zeta (0)} = {{\frac{1}{2}\frac{\omega_{x0} - \omega_{L}}{\omega_{L}}} = {\frac{1}{2}\frac{\frac{x_{0}}{L}}{1 - \frac{x_{0}}{L}}}}} & (18)\end{matrix}$

From Expression (18), which represents the maximum damping ratio whenthe normalized negative stiffness value is zero, it is found that themaximum damping ratio is determined by the ratio of the position x₀where the vibration damping device is disposed to the length L of themain rope 16 (hereinafter simply referred to as the ratio). It is alsofound that when the length L of the main rope 16 becomes greater and theratio becomes smaller, the numerator of Expression (18) becomes smallerand thus, the maximum damping ratio also becomes smaller. That is, it isfound that vibration of the main rope 16, which is a long elevator rope,in a high rise building is difficult to control with a vibration dampingdevice that uses only viscosity. Therefore, the vibration damping device100 including the displacement amplifier 7 using negative stiffness ishighly effective.

Next, the vibration damping effect of the negative stiffness andviscosity will be examined from the above expression. FIG. 19 is a graphof the function of Expression (18) representing the maximum dampingratio, and illustrates the vibration damping effect of the vibrationdamping device configured with only viscosity and without theaforementioned negative stiffness. In the figure, the abscissa axisindicates the ratio x₀/L of the position x₀ where the vibration dampingdevice is disposed to the length L of the main rope 16, and the ordinateaxis indicates the maximum damping ratio. It is found that the maximumdamping ratio is proportional to the ratio x₀/L. However, when the ratiox₀/L is 0.01, for example, the maximum damping ratio ζ is 0.005, whichmeans that an increase in the absolute value is only a little.Therefore, the vibration damping effect is not expected in the regionwhere the ratio x₀/L is small.

In the elevator apparatus, provided that the position x₀ where thevibration damping device is disposed cannot be changed, since the ropelength L will change as the car 14 is raised or lowered, the ratio x₀/Lwill greatly change correspondingly. That is, if vibration damping isperformed using only viscosity, there is a disadvantage that theobtained performance is likely to vary depending on the rope length,that is, the position of the car 14.

FIG. 20 illustrates the maximum damping ratio when the ratio x₀/L of thedistance x₀ from the end B1 to the position where the vibration dampingdevice 100 is disposed to the length L of the main rope 16 is 0.01, andpositive or negative stiffness including that of the displacementamplifier 7 is applied. The graph of the figure is calculated based onExpression (17), and the abscissa axis indicates the normalized negativestiffness value K_(p) bar of the vibration damping device, and theordinate axis indicates the maximum damping ratio ζ. When the ratio x₀/Lis 0.01, if the vibration damping device is configured with only avibration damper using viscosity as in FIG. 19, the maximum dampingratio ζ is 0.005. Thus, only a small damping effect is obtained. In theabscissa axis of the figure, the direction in which the positive valueof the normalized stiffness value increases is the rightward direction.Thus, regarding the negative stiffness, the direction in which theabsolute value increases is the leftward direction.

In FIG. 20, as the absolute value of the normalized negative stiffnessvalue K_(p) bar increases from zero toward the boundary G1, the maximumdamping ratio increases hyperbolically. Meanwhile, when the normalizednegative stiffness value K_(p) bar is on the left side of −1, that is,when the absolute value thereof exceeds 1, the maximum damping ratio hasa large negative value. Further, as the absolute value of the normalizednegative stiffness value K_(p) bar increases, the absolute value of themaximum damping ratio on the negative side decreases but the maximumdamping ratio approaches zero from the negative side. From this graph,it is found that the boundary (G1) is present at a normalized stiffnessvalue of slightly greater than −1. Herein, when the normalized stiffnessvalue is changed from zero to the negative side, the maximum dampingratio suddenly increases to the positive side and is then inverted tothe negative side. Thus, the boundary of the normalized stiffness valueat which the maximum damping ratio changes from positive to negative isdefined as the boundary G1. Then, it is found that as the normalizednegative stiffness value K_(p) bar approaches the value at the boundaryG1, the maximum damping ratio increases.

Herein, comparing the vibration damping illustrated in FIG. 20 with thevibration damping of the vibration damping device configured with only avibration damper illustrated in FIG. 19 can confirm that the maximumdamping ratio in FIG. 20 is significantly increased. Further, using thenegative stiffness portion 71 with negative stiffness characteristics,which is the displacement amplifier 7, can increase the displacement ofthe main rope 16 and allow the displacement to have characteristicscloser to the characteristics of the antinode of the vibration.

The effect of the negative stiffness characteristics of the negativestiffness portion 71 greatly depends on the distance x₀ from the end B1or B2 of the rope to the position where the vibration damping device 100is disposed, and has low sensitivity to the length L of the main rope16. Thus, the robustness of the damper as the vibration damping meanscan also be increased.

Herein, when the absolute value of the normalized negative stiffnessvalue becomes greater than that at the boundary G1, the value of themaximum damping ratio becomes negative. That is, it is found that aregion indicated by G2 in which the normalized negative stiffness valueis less than −1 is an unstable region. The value of the normalizednegative stiffness value at the boundary G1 is the value of K_(p) bar atwhich the damping ratio is infinite in Expression (17), and isrepresented by the following expression.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 19} \right. & \; \\{\left| {\overset{\_}{K}}_{p}^{asy} \right| = {\left| {{- \frac{1}{\alpha}}\frac{\omega_{L}^{2}}{\omega_{x0}^{2}}} \right| = \frac{L}{L - x_{0}}}} & (19)\end{matrix}$

Expression (19) represents that the absolute value of the normalizednegative stiffness value at the boundary G1 is the value obtained bydividing the length of the main rope 16 by the difference between thelength of the main rope 16 and the distance from the end B1 to theposition where the vibration damping device is disposed. That is, whenthe vibration damping device 100 is provided near the traction machineof the elevator, the absolute value of the normalized negative stiffnessvalue at the boundary G1 is the value obtained by dividing the length ofthe main rope 16 by the distance from the vibration damping device 100to the car 14. Alternatively, when the vibration damping device 100 isprovided near the car 14 of the elevator, the absolute value of thenormalized negative stiffness value at the boundary G1 is the valueobtained by dividing the length of the main rope 16 by the distance fromthe vibration damping device 100 to the traction machine.

It should be noted that the length of the main rope 16 is the length ofthe main rope 16 from its end in contact with the sheave of the tractionmachine to the car 14. Thus, the length of the main rope 16 will changeas the car 14 of the elevator is raised and lowered. Therefore, theabsolute value of the normalized negative stiffness value at theboundary G1 becomes large when the car 14 is at the top floor andbecomes small when the car 14 is at the bottom floor.

Accordingly, if the vibration damping device 100 is configured such thatit has the resultant stiffness value with an absolute value less thanthat of the normalized negative stiffness value obtained by dividing“the length of the main rope 16 when the car 14 is at the bottom floor”by “the difference between the length of the main rope 16 and thedistance from the end B1 to the position where the vibration dampingdevice is disposed,” an unstable condition can be reliably avoided.Therefore, if the negative stiffness portion 71 (i.e., the displacementamplifier 7) and the limiting members are configured such that theabsolute value of the resultant stiffness of the vibration dampingdevice 100 does not become greater than the value obtained by dividing“the length of the main rope 16 when the car 14 is at the bottom floor”by “the difference between the length of the main rope 16 and thedistance from the end B1 to the position where the vibration dampingdevice is disposed” and also such that the resultant stiffness value ofthe vibration damping device 100 becomes as small as possible, anunstable condition can be avoided and a device with a high vibrationdamping effect can be obtained.

In addition, a region G4 illustrated in FIG. 20 is a region where thestiffness value of the stiffness member of the vibration damping device100 is positive. In the region G4, the maximum damping ratio is zero.Therefore, in comparison with the characteristics of the maximum dampingratio of the damping device that uses only viscosity in FIG. 18, themaximum damping ratio obtained herein becomes smaller than that whenonly viscosity is used. Thus, implementation of positive stiffness isnot preferred. Therefore, to control vibration of the main rope 16, itis desirable to implement a normalized negative stiffness value in therange of the following expression.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 20} \right\rbrack & \; \\{{- \frac{L}{L - x_{0}}} < {\overset{\_}{K}}_{p} < 0} & (20)\end{matrix}$

Expression (20) represents that the normalized negative stiffness valueK_(p) bar is greater than the normalized negative stiffness value at theboundary G1 represented by Expression (19) and is less than zero. SinceK_(p) bar means that the negative stiffness value has been divided bythe constant G of Expression (11) above for normalization, the negativestiffness value to be implemented can be determined by multiplyingExpression (20) by the constant G.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 21} \right\rbrack & \; \\{{{- \frac{T}{x_{0}}}\frac{L}{L - x_{0}}} < K_{p} < 0} & (21)\end{matrix}$

The present embodiment is designed to fix a negative stiffness value inthe stable region represented by Expression (21) using the limitingmembers so as to maximally extract the damping effect by means ofviscosity. The left-hand side of Expression (21) corresponds to theslope of the solid line a in FIG. 5 described in Embodiment 1. The slopeof the solid line a in FIG. 5 represents the minimum negative stiffness(i.e., the maximum stiffness in terms of the absolute value of astiffness force) that does not cause an unstable condition due to thenegative stiffness portion 71. Specifically, the minimum negativestiffness that ensures stability is obtained by multiplying a value,which is obtained by dividing the tension of the main rope by theposition where the vibration damping device is disposed, by a correctioncoefficient including the length of the main rope and the position wherethe vibration damping device is disposed.

Expression (21) represents the desired range of the negative stiffnessvalue K_(p) of the negative stiffness portion 71 of the displacementamplifier 7. Similarly, Expression (19) represents the normalizednegative stiffness value at the boundary G1. When Expression (19) ismultiplied by the constant G of Expression (11) to obtain a negativestiffness value, the following expression is obtained.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 22} \right\rbrack & \; \\{K_{p}^{asy} = {{- \frac{T}{x_{0}}}\frac{L}{L - x_{0}}}} & (22)\end{matrix}$

Expression (22) represents the negative stiffness value K_(p) ^(asy) atthe boundary between the stable and unstable regions of the displacementamplifier 7 of the vibration damping device 100. It should be noted thatthe superscript asy means an asymptote. Similar to the above descriptionmade with reference to Expression (19), if the negative stiffnessportion 71 (i.e., the displacement amplifier 7) and the limiting membersare configured such that the resultant stiffness value of the vibrationdamping device 100 does not become smaller than the negative stiffnessvalue of Expression (22) that is represented by the tension T, thedistance x₀ from the end B to the position where the vibration dampingdevice is disposed, and the length L of the main rope 16 when the car 14is at the bottom floor, but becomes as large as possible, an unstablecondition can be avoided and a device with a high vibration dampingeffect can be provided.

Further, regarding the limiting members 8 b in FIG. 15, the rollers atthe tips of the limiting members 8 b are controlled to come into contactwith the main rope 16 based on the distance between the permanentmagnets 24 and the main rope 16 a so that the attraction force of thepermanent magnets 24 as the displacement amplifier does not becomesmaller than the negative stiffness value K_(p) ^(asy) represented byExpression (22). Accordingly, the attraction force (i.e., negativestiffness force) of the permanent magnets 24 as the displacementamplifier can stably amplify a displacement without the vibrationdamping device 100 entering the unstable region.

Furthermore, regarding the limiting members 8 c in FIG. 17, the limitingmembers 8 c are provided at positions where they contact the limitingmembers 8 c in a state where the negative stiffness force exerted by thetoggle link mechanism 31 does not become smaller than the negativestiffness value K_(p) ^(asy) represented by Expression (22).Accordingly, the negative stiffness force of the toggle link mechanism31, which is the displacement amplifier, can stably amplify adisplacement without the vibration damping device 100 entering theunstable region.

Regarding the tension T of the main rope 16, the negative stiffnessvalue K_(p) ^(asy) at the boundary may be determined with the tension ofthe main rope 16 when the car 14 is empty, and the determined value maybe used as the resultant stiffness value of the vibration damping device100. The tension of the main rope 16 is the lowest when the car 14 isempty. Therefore, the negative stiffness value K_(p) ^(asy) at theboundary is the smallest when the car 14 is empty. Setting the resultantstiffness value of the vibration damping device 100 in this manner canavoid an unstable condition and thus is safe.

The above holds true for not only the main rope 16 between the tractionmachine and the car 14 but also the traction machine, the counterweight15, the governor rope, the traveling cable, and other elevator ropes.

According to the present embodiment, the elevator apparatus 11 includesthe vibration damping device 100. The vibration damping device 100reduces vibration of an elevator rope. That is, a structure that is avibration control target of the vibration damping device 100 of thepresent embodiment is an elevator rope. In particular, the vibrationdamping device 100 is directed to control vibration of the main rope 16of the elevator that is connected to the car 14 and the counterweight 15of the elevator and is wound on the sheave, as a target elevator rope.The vibration damping device 100 according to the present embodimentincludes the displacement amplifier 7 that is arranged along anyposition in the longitudinal direction of the elevator rope and thatamplifies a displacement of the elevator rope, and the limiting membersthat control the displacement amplification performed by thedisplacement amplifier 7 such that the displacement of the elevator ropeamplified by the displacement amplifier 7 does not become greater thanthe preset first displacement. Such a configuration can stably increasea displacement due to vibration of the elevator rope at the positionwhere the displacement amplifier 7 is provided, and thus can increasethe vibration damping effect.

Further, the vibration damping device 100 of the present embodimentincludes the limiting members that allow a force exerted by thedisplacement amplifier 7 to be smaller than a force with which theelevator rope attempts to return to the equilibrium position with thetension of the elevator rope. This can stably increase a displacementdue to vibration of the elevator rope at the position where thedisplacement amplifier 7 is provided, and thus can increase thevibration damping effect.

The displacement amplifier 7 of the vibration damping device 100 of thepresent embodiment includes the negative stiffness member that exerts aforce corresponding to a transverse displacement of the elevator rope ina direction away from the equilibrium position of the elevator rope.Therefore, the transverse vibration of the elevator rope can beeffectively controlled.

Further, the displacement amplifier 7 of the vibration damping device100 of the present embodiment is arranged at a position closer to thesheave than to the car 14 or the weight. Therefore, even at a positionwhere a transverse displacement of the elevator rope is small, thedisplacement amplifier 7 can increase the displacement and change thevibration mode, and thus can effectively control the vibration.

The distance between the position of the displacement amplifier 7 of thevibration damping device 100 of the present embodiment and the positionof the car 14 or the counterweight 15, or the sheave is shorter than thedistance between both fixed positions of the elevator rope. In addition,the distance between the position of the displacement amplifier 7 andthe position of the car 14 or the counterweight 15, or the sheave isgreater than zero. Accordingly, even at a position where a displacementof the elevator rope is small, the displacement amplifier 7 can increasethe displacement and can change the vibration mode so that the vibrationdamping device 100 can effectively control the vibration.

The first displacement based on which the limiting members of thevibration damping device 100 of the present embodiment control thedisplacement amplification performed by the displacement amplifier 7 isa displacement where a force is exerted with a modulus of elasticitythat has a value obtained by dividing the tension acting on the elevatorrope when the car 14 in an empty state is at the top floor of theelevator by the distance from the fixed position of the elevator rope tothe position coupled to the displacement amplifier 7. Accordingly, thevibration damping device 100 can always and stably increase adisplacement of the elevator rope and thus can increase the vibrationdamping effect.

The displacement amplifier 7 and the limiting members of the vibrationdamping device 100 of the present embodiment amplify a displacement ofthe main rope 16 by exerting a force based on the modulus of elasticityK. The modulus of elasticity K satisfies an inequality represented byExpression (23). Herein, the tension of the elevator rope is T, thedistance from the connection point between the car 14 or the weight andthe elevator rope to the position where the displacement amplifier 7 isarranged is x₀, and the total length of the elevator rope is L.Accordingly, the vibration damping device 100 can always and stablyincrease a displacement of the elevator rope, and thus can increase thevibration damping effect.

$\begin{matrix}\left\lbrack {{Math}.\mspace{14mu} 23} \right\rbrack & \; \\{{{- \frac{T}{x_{0}}}\frac{L}{L - x_{o}}} < K < 0} & (23)\end{matrix}$

The displacement amplifier 7 may include the pair of magnet units 54.The pair of magnet units 54 are arranged with their magnetic polesfacing each other across the elevator rope. The limiting members 8 a area pair of non-magnetic bodies arranged between the magnetic poles of thepair of magnet units 54 and the elevator rope. Each limiting member 8 acontrols the approach of the elevator rope to the magnetic pole of eachof the pair of magnet units 54 so that the elevator rope does not becomeclose to the magnetic pole beyond the thickness of the limiting member 8a. Therefore, by forming each limiting member 8 a thicker than thethickness at which the main rope 16 contact the limiting member 8 a whenthe main rope 16 is displaced by the first displacement, it becomespossible for the vibration damping device 100 to stably controlvibration of the elevator rope. In addition, the displacement amplifier7 amplifies a displacement of the elevator rope without contact.Accordingly, wear of the elevator rope and the like due to amplificationof the displacement can be suppressed.

The pair of magnet units 54 are arranged with their same magnetic polesfacing each other. Accordingly, the pair of magnet units 54 repel eachother. Therefore, the gap between the pair of magnet units 54 is notclosed by the magnetic forces of the pair of magnet units 54. Thus, itis not necessary to consider an attraction force acting between the pairof magnet units 54 when fixing the pair of magnet units 54.

Each of the pair of magnet units 54 includes the yoke 25, the permanentmagnet 24 a, and the permanent magnet 24 b. The yoke 25 is arrangedalong a direction parallel with the elevator rope. The magnetic poles ofthe permanent magnet 24 a are directed toward one end of the yoke 25from the direction of the elevator rope. The magnetic poles of thepermanent magnet 24 b are opposite to those of the permanent magnet 24 aand are directed toward the other end of the yoke 25 from the samedirection of the permanent magnet 24 a. Accordingly, the yoke 25 guidesa magnetic flux emitted from the magnetic pole on the side opposite tothe elevator rope toward the inside. Thus, each magnet unit 54 can havesuppressed leakage of the magnetic flux on the side opposite to theelevator rope. This can suppress the influence of the vibration dampingdevice 100 on the peripheral devices.

The displacement amplifier 7 may include an unstable link mechanism thatgenerates a negative stiffness force upon occurrence of displacement ofone or more links. In such a case, the limiting member 8 c controls thedisplacement of at least one of the one or more links. Accordingly, thedisplacement amplifier 7 can generate a negative stiffness force withoutusing a magnetic force.

The link mechanism of the displacement amplifier 7 may be a pair oftoggle link mechanisms 31 arranged across the elevator rope.Accordingly, the displacement amplifier 7 can generate a negativestiffness force using a simple mechanism.

The displacement amplifier 7 may include rollers to come into contactwith the elevator rope. Accordingly, deterioration that would occur dueto friction between the elevator rope and the displacement amplifier 7can be suppressed.

The vibration damping device 100 may include a vibration damper thatreduces vibration of the elevator rope. Accordingly, vibration energy isdissipated efficiently. Thus, a high vibration damping effect can beobtained.

The vibration damper includes the coil 26 and the electric resistor 27,for example. The coil 26 passes a magnetic flux passing through at leastone of the pair of magnet units 54. The electric resistor 27 iselectrically connected to the coil 26. The coil 26 may be wound on theyoke 25 of at least one of the pair of magnet units 54. Accordingly,amplification of displacement by the displacement amplifier 7 anddissipation of vibration energy by the vibration damper are performedconcurrently. Thus, the vibration damping device 100 can moreeffectively control vibration of the elevator rope using a simplestructure.

The vibration damping device 100 of the present embodiment is alsoapplicable to longitudinal vibration of the main rope 16. FIG. 21illustrates an exemplary configuration of a vibration damping devicethat controls longitudinal vibration of the main rope 16. The main rope16 a is fixed to an upper beam 34 of a car via a shackle rod 36 and ashackle spring 35. A ferromagnetic body 37 is attached to an end of theshackle rod, and magnets 24 are provided on the upper beam 34 of the carso as to face the ferromagnetic body 37. With such a configuration,negative stiffness characteristics can be imparted in the x-direction(i.e., the vertical direction). In addition, limiting members 38 areprovided to prevent an unstable condition. It should be noted thatlongitudinal vibration has a smaller amplitude than transversevibration. Thus, the limiting members 38 may be removed if the vibrationdamping device 100 operates only in a region where the nonlinearity ofthe displacement amplifier is not strong. Further, as the element forimplementing the negative stiffness portion 71, a toggle link mechanismmay be used instead of the permanent magnets 24.

Each limiting member of the vibration damping device 100 of the presentembodiment includes a roller to come into contact with the elevatorrope. Such a roller is effective in reducing friction between theelevator rope and the limiting member and thus preventing deteriorationof both the members.

FIG. 22 is a view of the vibration damping device 100 of the presentembodiment applied to the elevator apparatus 11 including a plurality ofmain ropes 16. Herein, the structure 1 whose vibration is controlled bythe vibration damping device 100 is the plurality of main ropes 16. Anend of each of the plurality of main ropes 16 is connected to the top ofthe car 14. The vibration damping device 100 is provided above the car14. The vibration damping device 100 includes a support base 50 and arestraining member 51.

The support base 50 is provided on the top of the car 14. The supportbase 50 is provided around the plurality of main ropes 16.

The restraining member 51 is made of a ferromagnetic material. Therestraining member 51 is a member that maintains a constant distancebetween each of the plurality of main ropes 16 in the horizontaldirection. The restraining member 51 is a block-like member fixed toeach of the plurality of main ropes 16, for example.

The vibration damping device 100 includes at least three magnet units54. In this example, the vibration damping device 100 includes fourmagnet units 54. Each of the plurality of magnet units 54 is provided onthe upper face of the support base 50. Each of the plurality of magnetunits 54 includes permanent magnets 24 (24 a and 24 b). The magneticpoles of the plurality of magnet units 54 are arranged facing therestraining member 51 from different directions so as to surround therestraining member 51. For example, when the vibration damping device100 includes three magnet units, the magnetic poles of the plurality ofmagnet units 54 may be arranged at intervals of 120° with respect to thecentral axis of the restraining member 51 along the longitudinaldirection of the main ropes 16. Meanwhile, when the vibration dampingdevice 100 includes four magnet units, the magnetic poles of theplurality of magnet units 54 may be arranged at intervals of 90° withrespect to the central axis of the restraining member 51 along thelongitudinal direction of the main ropes 16. The plurality of magnetunits 54 may be arranged at different heights along the longitudinaldirection of the main ropes 16.

As described above, when the structure 1 whose vibration is controlledby the vibration damping device 100 is the plurality of main ropes 16,the vibration damping device 100 includes the restraining member 51. Therestraining member 51 maintains a constant distance between each of theplurality of main ropes 16 in the horizontal direction. The design valueof the negative stiffness value of the negative stiffness portion 71 isdetermined by the tension of an elevator rope as indicated by Expression(11). Therefore, when the vibration damping device 100 is to controlvibration of the plurality of main ropes 16, the vibration dampingperformance of the vibration damping device 100 would decrease if thetension varies among the plurality of main ropes 16. Therefore, theplurality of main ropes 16 are integrated by being restrained by therestraining member 51, whereby the design value of the negativestiffness value of the negative stiffness portion 71 is determined bythe total tension of the plurality of main ropes 16. The tensions of theplurality of main ropes 16 vary both positively and negatively.Therefore, the total sum of variation in the tension of each of theplurality of main ropes 16 has no (i.e., cancelled) influence of thevariation in the tension of each of the plurality of main ropes 16. Thiscan reduce a decrease in the vibration damping performance due tovariation in the tension of each of the plurality of main ropes 16.Further, the robustness of the vibration damping performance of thevibration damping device 100 against variation in the tension of each ofthe plurality of main ropes 16 improves.

Further, the restraining member 51 is fixed to each of the plurality ofmain ropes 16. Accordingly, the restraining member 51 is configured witha simple structure, such as a block-like member.

The influence of the position of the car 14 will be described withreference to FIGS. 23. FIG. 23(a) illustrates a state where the car 14is stopped at the bottom floor. FIG. 23(b) illustrates a state where thecar 14 is stopped at the top floor.

As illustrated in FIG. 23(a), when the elevator apparatus 11 includes aplurality of main ropes 16, for example, the main ropes 16 are attachedto the car 14 at a plurality of different positions. Therefore, theplurality of main ropes 16 are stretched at a fleet angle θ from the endB1 to the car 14.

As illustrated in FIG. 23(b), the fleet angle θ changes depending on thedistance between the car 14 and the traction machine 12. The distancebetween the car 14 and the traction machine 12 is the shortest when thecar 14 is stopped at the top floor. At this time, the fleet angle θ isthe largest. When the fleet angle θ changes, the distance between theplurality of main ropes 16 spreading from the end B1 at the fleet angleθ and the negative stiffness portion 71 will also change. Even when themain ropes 16 are not vibrating, there may be cases where the horizontalpositions of the main ropes 16 as viewed from the negative stiffnessportion 71 change. At this time, if the moving quantity of the mainropes 16 in the horizontal direction is large, the main ropes 16 maycome into contact with the permanent magnets 24 of the negativestiffness portion 71.

FIG. 24 is a view illustrating the vibration damping device 100 when thecar 14 is stopped at the bottom floor. In FIG. 24, the main rope 16 a isat the equilibrium position. At this time, the main rope 16 a passesthrough the center of the rope duct 28 a. In such a state, the fleetangle θ is the smallest.

FIG. 25 is a view illustrating the vibration damping device 100 when thecar 14 is stopped at the top floor. In FIG. 25, the main rope 16 a is atthe equilibrium position. The main rope 16 a is stretched between thetraction machine 12 and the car 14 at a fleet angle θ larger than thatwhen the car 14 is at the bottom floor. At this time, the main rope 16 ais located closer to the permanent magnets 24 of the negative stiffnessportion 71 than when the car 14 is stopped at the bottom floor. Inaddition, the permanent magnets 24 further attract the main rope 16 witha force stronger than that when the car 14 is stopped at the bottomfloor. Accordingly, the allowance for the main rope 16 a between theequilibrium position and the first displacement becomes smaller. Thismay result in a smaller range of displacement of the main rope 16 whosevibration is controlled by the vibration damping device 100 with achange in the fleet angle θ along with a change in the position of thecar 14.

Next, an example of the vibration damping device 100 that suppresses theinfluence of the fleet angle θ will be described with reference to FIGS.26 and 27. FIG. 26 is a top view of the vibration damping device 100.FIG. 27 is a side view of the vibration damping device 100. A pluralityof main ropes 16 are aligned in the horizontal direction. The pluralityof main ropes 16 are arranged in the direction of the rotation axis ofthe traction machine 12, for example.

As illustrated in FIG. 26, the vibration damping device 100 includes arestraining member 51 and a base 52. The vibration damping device 100 isprovided in the machine room 29, for example.

The restraining member 51 includes a pair of rollers 53. The rotationaxis of each of the pair of rollers 53 is oriented in the directionparallel with the direction in which the plurality of main ropes 16 arearranged. The pair of rollers 53 contact each of the plurality of mainropes 16 from both sides thereof in the direction perpendicular to therotation axes. Each of the pair of rollers 53 has groove-like guidesformed on the side face thereof so as to keep a constant distancebetween each of the plurality of main ropes 16 in the horizontaldirection.

As illustrated in FIG. 27, the base 52 is provided so as to cover thenegative stiffness portion 71 from above. The upper face of the base 52is a horizontal plane.

The restraining member 51 is provided on the base 52. The restrainingmember 51 is provided on the upper face of the base 52 so as to befreely displaced in the horizontal plane in the direction perpendicularto the direction in which the plurality of main ropes 16 are arranged.

As described above, when the plurality of main ropes 16 are aligned inthe horizontal direction, the restraining member 51 includes the pair ofrollers 53. The pair of rollers 53 each have a rotation axis parallelwith the direction in which the plurality of main ropes 16 are arranged.The pair of rollers 53 contact each of the plurality of main ropes 16from both sides thereof in the direction perpendicular to the rotationaxes. The restraining member 51 squeezes each of the plurality of mainropes 16 with the pair of rollers 53 above the displacement amplifier 7.Accordingly, the positions (i.e., moving quantities) of the main ropes16 change from the positions indicated by the dashed lines to thepositions indicated by the solid lines. This can avoid a contact betweenthe vibration damping device 100 and the main ropes 16. Further, sincethe influence of the position of the car 14 on the distance between thevibration damping device 100 and the main ropes 16 is reduced,fluctuation of the vibration damping effect of the vibration dampingdevice 100 due to the position of the car 14 is also reduced. Thus, thevibration damping device 100 can stably control vibration of theelevator ropes.

Next, another example of the vibration damping device 100 will bedescribed with reference to FIG. 28. In this example, the restrainingmember 51 is provided between the pair of magnet units 54. Therestraining member 51 is provided on the machine room floor 28. Therestraining member 51 is provided on the machine room floor 28 so as tobe freely displaced in the horizontal plane in the directionperpendicular to the direction in which the plurality of main ropes 16are arranged. The restraining member 51 has magnetic bodies on bothsides thereof in the direction in which it can be displaced on themachine room floor 28.

Accordingly, the installation space for the vibration damping device 100in the vertical direction can be suppressed. Further, the distancebetween the restraining member 51 and each magnet unit 54 does notdepend on the position of the car 14 at the equilibrium position.Therefore, the vibration damping performance of the vibration dampingdevice 100 is stabilized.

FIG. 29 is a view illustrating an example of the vibration dampingdevice 100 that controls vibration of the traveling cable 22. One end ofthe traveling cable 22 is connected to a hoistway-side terminal 48 b onthe inner wall of the hoistway. The car-side terminal at the other endof the traveling cable 22 is connected to the car 14. The portion of thetraveling cable 22 on the side connected to the car 14 is fixed theretovia a fixing portion 48 a. The fixing portion 48 a is provided at thebottom of the car 14, for example. If the car-side terminal of thetraveling cable 22 is connected to the top of the car 14, it may berouted to the fixing portion 48 a at the bottom of the car 14.

FIG. 30 are views each illustrating an exemplary configuration of thevibration damping device 100 that controls vibration of the travelingcable 22. In FIG. 30(a), the vibration damping device 100 is provided onthe fixing portion 48 a at the bottom of the car 14. The vibrationdamping device 100 includes the pair of magnet units 54 and the limitingmembers 8 a, for example. When the traveling cable 22 is formed of amagnetic material, such as iron, vibration of the traveling cable 22 iscontrolled with the magnetic forces received from the magnet units 54.Meanwhile, when the traveling cable 22 is formed of a non-magneticmaterial, such as copper, for example, the traveling cable 22 may becovered with a ferromagnetic material, for example. Accordingly,vibration of the traveling cable 22 is controlled with the magneticforces received from the magnet units 54 by the ferromagnetic material.

The vibration damping device 100 may also control vibration of thetraveling cable 22 using an unstable link mechanism, such as a togglelink mechanism, for example. In such a case, the vibration dampingdevice 100 may include a base on which the link mechanism is mounted ata position below the fixing portion 48 a. A force applied to the linkmechanism may be any of the weight of a weight, the elastic force of aspring, or a magnetic force, for example.

As illustrated in FIG. 30(b), the vibration damping device 100 may alsobe provided on the hoistway-side terminal 48 b. Alternatively, thevibration damping device 100 may be provided on each of the fixingportion 48 a and the hoistway-side terminal 48 b.

As described above, the vibration damping device 100 is directed tocontrol vibration of the traveling cable 22, which is connected to thecar 14 of the elevator, as a target elevator rope. The displacementamplifier 7 is arranged along any position in the longitudinal directionof the traveling cable 22. The displacement amplifier 7 amplifies adisplacement of the traveling cable 22. The limiting members 8 controlthe displacement amplification performed by the displacement amplifier 7such that the displacement of the traveling cable 22 amplified by thedisplacement amplifier 7 does not become greater than the firstdisplacement. Thus, vibration of the traveling cable 22 is reduced.

Embodiment 3

The present embodiment will describe the vibration damping device 100that controls vibration of an elevator rope wound on one or more sheavesof an elevator and folded thereover.

FIG. 31 is a configuration view of an elevator apparatus according toEmbodiment 3. FIG. 31 schematically illustrates the elevator apparatus11 in a state where there is no building sway and thus no vibration isgenerated. In this example, the elevator apparatus 11 is a 2:1 ropingelevator.

The elevator apparatus 11 includes a traction machine 12 and a deflectorsheave 13. A car 14 for carrying passengers has a car suspension sheave39 a at the top. A counterweight 15 has a counterweight suspensionsheave 39 b at the top. Both ends of a main rope 16 are fixed to the topof the hoistway with rope supports 55. The main rope 16 is wound on thecar suspension sheave 39 a, the traction machine 12, the deflectorsheave 13, and the counterweight suspension sheave 39 b in this order ina region from the rope support 55 on the side of the car 14 to the ropesupport 55 on the side of the counterweight 15.

FIG. 32 is a configuration view of the elevator apparatus according toEmbodiment 3. FIG. 32 illustrates a state where building sway 23 occursin the elevator apparatus 11 due to turbulence, such as earthquakes orwinds, for example. When the building sway 23 occurs, the tractionmachine 12, the deflector sheave 13, and the governor 19 (notillustrated in FIG. 32) fixed to the building also sway in a similarmanner. Accordingly, the main rope 16, the compensating rope 17, thegovernor rope 20, and the traveling cable 22, which are the elevatorropes, are vibrated. At this time, if the vibration frequency of thebuilding sway 23 coincides with the natural frequency of any of theelevator ropes, the sway of the elevator rope increases due to theresonance phenomenon. FIG. 32 exemplarily illustrates a state where thenatural frequency of the main rope 16 b coincides with the vibrationfrequency of the building sway, and thus a resonance phenomenon occurson the main rope 16 b.

FIGS. 33 and 34 each illustrate the vibration damping device 100provided on a housing 40 of the car suspension sheave 39 a. FIGS. 33 and34 are side views of the vibration damping device according toEmbodiment 3.

As illustrated in FIG. 33, the main rope 16 is wound on the carsuspension sheave 39 a in a region between a first portion R1 and asecond portion R2 of the main rope 16. The first portion R1 of the mainrope 16 is a portion drawn from the car suspension sheave 39 a that is asheave. The second portion R2 of the main rope 16 is a portion drawnfrom the car suspension sheave 39 a. The second portion R2 is drawn fromthe side opposite to the first portion R1. The first portion R1 and thesecond portion R2 are drawn in directions in parallel with each other.

The vibration damping device 100 includes the displacement amplifier 7and the limiting members 8 a.

In the present embodiment, the displacement amplifier 7 is a passivedevice. The displacement amplifier 7 is arranged around a region fromthe first portion R1 to the second portion R2 of the main rope 16. Thedisplacement amplifier includes a pair of outer magnet units 56 and aninner magnet unit 57.

The displacement amplifier 7 may include at least one of the pair ofouter magnet units 56 or the inner magnet unit 57. The outer magnetunits 56 and the inner magnet unit 57 may be arranged at differentheights along the longitudinal direction of the main rope 16. Inaddition, more than one outer magnet unit 56 and more than one innermagnet unit 57 may be arranged along the longitudinal direction of themain rope 16.

Each of the pair of outer magnet units 56 is a single permanent magnet,for example. The pair of outer magnet units 56 are arranged on the outerside of the first portion R1 and the second portion R2 of the main rope16 in the direction in which the first portion R1 and the second portionR2 are connected horizontally. The pair of outer magnet units 56 arearranged with their magnetic poles facing each other.

The inner magnet unit 57 is a single permanent magnet, for example. Theinner magnet unit 57 is arranged on the inner side of the first portionR1 and the second portion R2 of the main rope 16. One of the magneticpoles of the inner magnet unit 57 faces one of the magnetic poles of oneof the pair of outer magnet units 56 across the first portion R1 of themain rope 16. The other magnetic pole of the inner magnet unit 57 facesone of the magnetic poles of the other of the pair of outer magnet units56 across the second portion R2 of the main rope 16.

The limiting members 8 a are a set of non-magnetic bodies, for example.Some of the non-magnetic bodies of the limiting members 8 a are providedbetween the magnetic poles of the pair of outer magnet units 56 and themain rope 16. The others of the non-magnetic bodies of the limitingmembers 8 a are provided between the magnetic poles of the inner magnetunit 57 and the main rope 16. The thickness of the non-magnetic body ofeach limiting member 8 a is set so that the main rope 16 will come intocontact with the limiting member 8 a when the main rope 16 is displacedby the first displacement, for example.

As illustrated in FIG. 34(a), the inner magnet unit 57 has the S-polefacing the first portion R1 of the main rope 16. The outer magnet unit56 that faces the S-pole of the inner magnet unit 57 has the S-polefacing the first portion R1 of the main rope 16. The inner magnet unit57 has the N-pole facing the second portion R2 of the main rope 16. Theouter magnet unit 56 that faces the N-pole of the inner magnet unit 57has the N-pole facing the second portion R2 of the main rope 16. Thatis, the inner magnet unit 57 is arranged such that its S-pole faces theS-pole of one of the pair of outer magnet units 56 and its N-pole facesthe N-pole of the other of the pair of outer magnet units 56. Asillustrated in FIG. 34(b), the pair of outer magnet units 56 and theinner magnet unit 57 may be arranged with the S-poles and the N-polesexchanged.

When the main rope 16 is vibrated upon occurrence of the building sway23, a displacement of the first portion R1 of the main rope 16 due tothe vibration is amplified by a magnetic field between one of the pairof outer magnet units 56 and the inner magnet unit 57. Meanwhile, adisplacement of the second portion R2 of the main rope 16 due to thevibration is amplified by a magnetic field between the other of the pairof outer magnet units 56 and the inner magnet unit 57. The main rope 16comes into contact with the limiting members 8 a when displaced by thefirst displacement. The limiting members 8 a control the displacementamplification performed by the displacement amplifier 7 such that thedisplacement of the first portion R1 amplified by the displacementamplifier 7 does not become greater than the first displacement. Thelimiting members 8 a also control the displacement amplificationperformed by the displacement amplifier 7 such that the displacement ofthe second portion R2 amplified by the displacement amplifier 7 does notbecome greater than the first displacement.

As described above, the elevator apparatus 11 includes the vibrationdamping device 100. The vibration damping device 100 reduces vibrationof an elevator rope wound on the sheave of the elevator and foldedthereover. The elevator rope is, for example, the main rope 16. Thevibration damping device 100 includes the displacement amplifier 7 andthe limiting members 8 a. The displacement amplifier 7 is arrangedaround a region from the first portion R1 to the second portion R2 ofthe main rope. The first portion R1 of the main rope 16 is a portiondrawn from the sheave. The second portion R2 of the main rope 16 is aportion drawn from the sheave and on the side opposite to the firstportion R1. The first portion R1 and the second portion R2 are drawn indirections in parallel with each other. The displacement amplifier 7amplifies a displacement of each of the first portion R1 and the secondportion R2 of the main rope 16. The displacement amplifier 7 amplifies adisplacement of each of the first portion R1 and the second portion R2of the main rope 16. The limiting members 8 a control the displacementamplification performed by the displacement amplifier 7 such that thedisplacement of the first portion R1 or the second portion R2 amplifiedby the displacement amplifier 7 does not become greater than the firstdisplacement. The first displacement is the displacement of the mainrope 16 by which the main rope 16 is not allowed to return to theequilibrium position of the vibration. Accordingly, it is possible tostably increase a displacement due to vibration of the main rope 16 atthe position where the displacement amplifier 7 is provided, and thusincrease the vibration damping effect.

The displacement amplifier 7 includes the pair of outer magnet units 56and the inner magnet unit 57. The pair of outer magnet units 56 arearranged on the outer side of the first portion R1 and the secondportion R2 of the main rope 16 in the first direction in which the firstportion R1 and the second portion R2 are connected horizontally. Thepair of outer magnet units 56 are arranged with their magnetic polesfacing each other. The inner magnet unit 57 is arranged on the innerside of the first portion R1 and the second portion R2. The inner magnetunit 57 is arranged such that both magnetic poles face the pair of outermagnet units 56. The limiting members 8 a are a set of non-magneticbodies arranged between the magnetic poles of the pair of outer magnetunits 56 and the main rope 16 and between the opposite magnetic poles ofthe inner magnet unit 57 and the main rope 16. Each limiting member 8 acontrols the approach of the main rope 16 to the magnetic pole of eachof the pair of outer magnet units 56 and the inner magnet unit 57 sothat the main rope 16 does not become close to the magnetic pole beyondthe thickness of the limiting member 8 a. Therefore, by forming eachlimiting member 8 a thicker than the thickness at which the main rope 16contact the limiting member 8 a when the main rope 16 is displaced bythe first displacement, it becomes possible for the vibration dampingdevice 100 to stably control vibration of the main rope 16. Thedisplacement amplifier 7 amplifies a displacement of the main rope 16without contact. Accordingly, wear of the main rope 16 and the like dueto amplification of the displacement can be suppressed. The inner magnetunit 57 amplifies displacements of both the first portion R1 and thesecond portion R2 of the main rope 16. Accordingly, it is possible toconfigure the vibration damping device 100 with a smaller number ofparts than providing a vibration damping device that individuallycontrols vibration of each of the first portion R1 and the secondportion R2 of the main rope 16.

The inner magnet unit 57 is arranged such that its S-pole faces theS-pole of one of the pair of outer magnet units 56 and its N-pole facesthe N-pole of the other of the pair of outer magnet units 56.Accordingly, each of the pair of outer magnet units 56 and the innermagnet unit 57 repel each other. Therefore, the gap between each of thepair of outer magnet units 56 and the inner magnet unit 57 is not closedby the magnetic force. Thus, it is not necessary to firmly fix the pairof outer magnet units 56 or the inner magnet unit 57 considering anattraction force that would act due to the magnetic force.

FIG. 35 is a side view of a vibration damping device according toEmbodiment 3. FIG. 35 illustrates another example of the vibrationdamping device 100. To efficiently amplify transverse displacement ofthe main rope 16, it is preferable that the main rope 16 be arranged atthe center of the gap between each of the pair of outer magnet units 56and the inner magnet unit 57. That is, the dimensions of the gapspreferably satisfy the conditions: l_(d1)=l_(d2) and l_(d3)=l_(d4).Herein, l_(d1) is the dimension of the gap between the first portion R1of the main rope 16 and the magnetic pole of the outer magnet unit 56facing the first portion R1. l_(d2) is the dimension of the gap betweenthe first portion R1 of the main rope 16 and the magnetic pole of theinner magnet unit 57 facing the first portion R1. l_(d3) is thedimension of the gap between the second portion R2 of the main rope 16and the magnetic pole of the inner magnet unit 57 facing the secondportion R2. l_(d4) is the dimension of the gap between the secondportion R2 of the main rope 16 and the magnetic pole of the outer magnetunit 56 facing the second portion R2. Herein, the pair of outer magnetunits 56 and the inner magnet unit 57 may also be arranged such that thedimensions of the gaps satisfy the condition:l_(d1)=l_(d2)=l_(d3)=l_(d4).

For example, the inner magnet unit 57 includes a permanent magnet 24 anda pair of magnetic bodies 47. The pair of magnetic bodies 47 arearranged on the respective magnetic poles of the permanent magnet 24.Herein, the magnetic poles of the inner magnet unit 57 are the planes ofthe pair of magnetic bodies 47 on the side opposite to the permanentmagnet 24. The thickness of each of the pair of magnetic bodies 47 isset to satisfy the conditions: l_(d1)=l_(d2) and l_(d3)=l_(d4) accordingto the diameter of the car suspension sheave 39 a and the length of thepermanent magnet 24, for example. The limiting members 8 a are providedon the magnetic poles of the inner magnet unit 57. The magnetic bodies47 are arranged between the magnetic poles of the permanent magnet 24and the respective limiting members 8 a.

As described above, the inner magnet unit 57 is arranged at a positionwhere the width of the gap between the inner magnet unit 57 and one ofthe outer magnet units 56 facing each other across the first portion R1of the main rope 16 is equal to the width of the gap between the innermagnet unit 57 and the other outer magnet unit 56 facing each otheracross the second portion R2 of the main rope 16. Herein, the width ofthe gap through which the first portion R1 of the main rope 16 passesbetween one of the outer magnet units 56 and the inner magnet unit 57 isequal to the width of the gap through which the second portion R2 of themain rope 16 passes between the other outer magnet unit 56 and the innermagnet unit 57. Accordingly, a transverse displacement of the main rope16 is amplified symmetrically on both sides. Thus, the transversedisplacement of the main rope 16 is efficiently amplified.

The inner magnet unit 57 includes the permanent magnet 24 and themagnetic bodies 47. The magnetic poles of the permanent magnet 24 arearranged along the first direction in which the first portion and thesecond portion of the elevator rope are connected horizontally. Themagnetic bodies 47 are arranged on the opposite magnetic poles of thepermanent magnet 24. The magnetic bodies 47 adjust the length of theinner magnet unit 57 in the first direction. Accordingly, the innermagnet unit 57 can be configured so that a transverse displacement ofthe main rope 16 is efficiently amplified according to the diameter ofthe car suspension sheave 39 a or the length of the permanent magnet 24,for example.

FIG. 36 is a side view of a vibration damping device according toEmbodiment 3. FIG. 36 illustrates another example of the vibrationdamping device 100. To allow a displacement amplification force toeffectively act against a transverse displacement of the main rope 16,it is preferable that the magnetomotive forces of the magnet unitsarranged on both sides of the main rope 16 be equal. Herein, themagnetomotive force of each magnet unit is determined by the lengthl_(m) of the magnet unit in the magnetic pole direction. That is, thelength of each of the pair of outer magnet units 56 in the magnetic poledirection is preferably equal to the length of the inner magnet unit 57in the magnetic pole direction.

The inner magnet unit 57 includes a permanent magnet 24 and a pair ofmagnetic bodies 47. The pair of magnetic bodies 47 are arranged on therespective magnetic poles of the permanent magnet 24. Herein, themagnetic poles of the inner magnet unit 57 are the planes of the pair ofmagnetic bodies 47 on the side opposite to the permanent magnet 24. Thethickness of each of the pair of magnetic bodies 47 is set so that theinner magnet unit 57 has the length l_(m) in the magnetic poledirection. The limiting members 8 a are provided on the respectivemagnetic poles of the inner magnet unit 57. The magnetic bodies 47 arearranged between the magnetic poles of the permanent magnet 24 and therespective limiting members 8 a.

Each of the pair of outer magnet units 56 includes a permanent magnet 24and a pair of magnetic bodies 47. The pair of magnetic bodies 47 arearranged on the respective magnetic poles of the permanent magnet 24.Herein, the magnetic poles of each of the pair of outer magnet units 56are the planes of the pair of magnetic bodies 47 on the side opposite tothe permanent magnet 24. The thickness of each of the pair of magneticbodies 47 is set so that the length of each of the pair of outer magnetunits 56 in the magnetic pole direction becomes equal to the lengthl_(m) of the inner magnet unit 57 in the magnetic pole direction. Thelimiting member 8 a is provided on one of the magnetic poles of each ofthe pair of outer magnet units 56. One of the magnetic bodies 47 isarranged between one of the magnetic poles of the permanent magnet 24and the limiting member 8 a.

As described above, the length of each of the pair of outer magnet units56 in the first direction in which the first portion and the secondportion of the elevator rope are connected horizontally is equal to thelength of the inner magnet unit 57 in the first direction. Accordingly,the magnetomotive forces of the magnet units arranged on both sides ofthe elevator rope become equal. This allows a displacement amplificationforce to effectively act against a transverse displacement of theelevator rope.

FIG. 37 are side views of vibration damping devices according toEmbodiment 3. FIG. 37 each illustrate another example of the vibrationdamping device 100. As illustrated in FIG. 37(a), each of a pair ofouter magnet units 56 includes an outer yoke 58, a first outer permanentmagnet 60 a, and a second outer permanent magnet 60 b. The outer yoke 58is arranged along a second direction that is parallel with the firstportion R1 or the second portion R2 of the main rope 16. The magneticpoles of the first outer permanent magnet 60 a are directed toward theupper end of the outer yoke 58 from the direction of the main rope 16.The magnetic poles of the second outer permanent magnet 60 b areopposite to those of the first outer permanent magnet 60 a and aredirected toward the lower end of the outer yoke 58 from the direction ofthe main rope 16. The magnetic poles of each of the outer magnet units56 are, for example, the magnetic poles of the first outer permanentmagnet 60 a and the second outer permanent magnet 60 b that do not facethe outer yoke 58.

The inner magnet unit 57 includes an inner yoke 59, a first innerpermanent magnet 61 a, and a second inner permanent magnet 61 b. Theinner yoke 59 is arranged along the second direction that is parallelwith the first portion R1 or the second portion R2 of the main rope 16.The first inner permanent magnet 61 a is arranged at the upper end ofthe inner yoke 59 such that its magnetic poles face the same magneticpoles of the respective first outer permanent magnets 60 a of the pairof outer magnet units 56. The second inner permanent magnet 61 b isarranged at the lower end of the inner yoke 59 such that its magneticpoles face the same magnetic poles of the respective second outerpermanent magnets 60 b of the pair of outer magnet units 56.

Each of the pair of outer magnet units 56 forms a magnetic field on theside of the main rope 16. The outer yoke 58 forms a magnetic circuitbetween the first outer permanent magnet 60 a and the second outerpermanent magnet 60 b. Therefore, a leakage flux is suppressed on theouter side of the pair of outer magnet units 56.

As described above, each of the pair of outer magnet units 56 includesthe outer yoke 58, the first outer permanent magnet 60 a, and the secondouter permanent magnet 60 b. The outer yoke 58 is arranged along thesecond direction that is parallel with the first portion or the secondportion of the elevator rope. The magnetic poles of the first outerpermanent magnet 60 a are directed toward one end of the outer yoke 58from the direction of the elevator rope. The magnetic poles of thesecond outer permanent magnet 60 b are opposite to those of the firstouter permanent magnet 60 a and are directed toward the other end of theouter yoke 58 from the same direction of the first outer permanentmagnet 60 a. The inner magnet unit 57 includes the inner yoke 59, thefirst inner permanent magnet 61 a, and the second inner permanent magnet61 b. The inner yoke 59 is arranged along the second direction. Thefirst inner permanent magnet 61 a is arranged at one end of the inneryoke 59 such that its magnetic poles face the same magnetic poles of therespective first outer permanent magnets 60 a of the pair of outermagnet units 56. The second inner permanent magnet 61 b is arranged atthe other end of the inner yoke 59 such that its magnetic poles face thesame magnetic poles of the respective second outer permanent magnets 60b of the pair of outer magnet units 56. Accordingly, the influence of aleakage flux from the magnet units of the displacement amplifier 7 onthe operation of the peripheral devices can be suppressed. Further, as aleakage flux is reduced, the amount of the magnetic flux directed towardthe elevator rope is increased. This allows a displacement of theelevator rope to be amplified more effectively. Thus, the vibrationdamping performance improves.

As illustrated in FIG. 37(b), the inner magnet unit 57 may include apair of permanent magnets 24 c at the upper end of the inner yoke 59.The pair of permanent magnets 24 c are arranged across the upper end ofthe inner yoke 59. The inner magnet unit 57 may also include a pair ofpermanent magnets 24 d at the lower end of the inner yoke 59. The pairof permanent magnets 24 d are arranged across the lower end of the inneryoke 59.

FIG. 38 is a side view of a vibration damping device according toEmbodiment 3. As illustrated in FIG. 38, the displacement amplifier 7may include a pair of magnet units 54 for each of the first portion R1and the second portion R2 of the main rope 16.

FIG. 39 is a side view of a vibration damping device according toEmbodiment 3. FIG. 39 illustrates another example of the vibrationdamping device 100. The vibration damping device 100 includes a magneticshield 46. The magnetic shield 46 is formed of a ferromagnetic material.Alternatively, the surface of the magnetic shield 46 is covered with aferromagnetic material. Accordingly, the magnetic shield 46 has aferromagnetic property. Herein, the ferromagnetic material used for themagnetic shield 46 is a material commonly used as a magnetic shieldmaterial, such as sheet metal or permalloy, for example.

As described above, the vibration damping device 100 includes themagnetic shield 46. The magnetic shield 46 has a ferromagnetic property.Accordingly, the influence of a leakage flux from the magnet units ofthe displacement amplifier 7 on the operation of the peripheral devicescan be suppressed.

FIG. 40 are side views of vibration damping devices according toEmbodiment 3. FIG. 40 each illustrate another example of the vibrationdamping device 100. As illustrated in FIG. 40(a), each of a pair ofouter magnet units 56 and an inner magnet unit 57 may include three ormore permanent magnets 24. The three or more permanent magnets 24 arearranged such that alternately opposite magnetic poles face the mainrope 16 in the direction along the main rope 16, for example.

An outer yoke 58 has grooves formed on its face on the side facing themain rope 16. The grooves of the outer yoke 58 have been machinedcorresponding to the shapes of the permanent magnets 24 of the outermagnet unit 56. Accordingly, it is possible to suppress the errantmutual attraction of a pair of permanent magnets 24, which are adjacentin the extending direction of the main rope 16, to each other due to anattraction force acting between the pair of permanent magnets 24.Therefore, the permanent magnets 24 can be attached easily.

As illustrated in FIG. 40(b), the displacement amplifier 7 may include apair of magnet units 54 each having three or more permanent magnets 24for each of the first portion R1 and the second portion R2 of the mainrope 16.

FIGS. 41 to 43 are views illustrating another example of the vibrationdamping device 100. FIG. 41 is a side view of a vibration damping deviceaccording to Embodiment 3. FIG. 42 is a perspective view of thevibration damping device according to Embodiment 3. FIG. 43 is a topview of the vibration damping device according to Embodiment 3.

The vibration damping device 100 includes a vibration damper. Thevibration damper includes coils 26 and electric resistors 27. Each coil26 is wound on each of the outer yoke 58 and the inner yoke 59. Eachelectric resistor 27 is electrically connected to the coil 26.

Herein, a magnetic flux passing through each of the outer yokes 58 andthe inner yoke 59 changes with a change in the displacement of the mainrope 16. Accordingly, a voltage is generated in each coil 26 due to anelectromagnetic induction phenomenon. Accordingly, a current flowsthrough each electric resistor 27. In this manner, the vibration energyof the main rope 16 is dissipated as Joule heat by the electric resistor27. Therefore, the vibration damper reduces the vibration of the mainrope 16.

FIG. 44 is a perspective view of a vibration damping device according toEmbodiment 3. FIG. 44 is a view illustrating another example of thevibration damping device 100. Herein, the structure whose vibration iscontrolled by the vibration damping device 100 is a plurality of mainropes 16. First portions R1 of the plurality of main ropes 16 arealigned in the horizontal direction in a vertical plane. In thisexample, the vertical plane is the xz plane. The plurality of main ropes16 are arranged in the z-direction. Second portions R2 of the pluralityof main ropes 16 are arranged in a vertical plane parallel with thevertical plane including the first portions R1 of the plurality of mainropes 16.

The magnetic poles of permanent magnets 24 of the displacement amplifier7 face the first portions R1 or the second portions R2 of the pluralityof main ropes 16 arranged in the horizontal direction. The magneticpoles of the permanent magnet 24 are arranged in parallel with thevertical plane including the first portions R1 or the second portionsR2. The horizontal width of each permanent magnet 24 is wider than thetotal width of the first portions R1 or the second portions R2 arrangedin the horizontal direction. Accordingly, displacements due to vibrationof the plurality of main ropes 16 can be amplified.

FIGS. 45 and 46 are views illustrating another example of the vibrationdamping device 100. FIG. 45 is a side view of a vibration damping deviceaccording to Embodiment 3. FIG. 46 is a top view of the vibrationdamping device according to Embodiment 3. As illustrated in FIG. 45, thedisplacement amplifier 7 may amplify a displacement of a first portionR1 or a second portion R2 using an unstable link mechanism. Thedisplacement amplifier 7 includes a pair of toggle link mechanisms 31and a rope restraining member 32 for each of the first portion R1 andthe second portion R2 of each main rope 16 a.

As illustrated in FIG. 46, each rope restraining member 32 includes apair of rollers 45. The pair of rollers 45 contact the plurality of mainropes 16 a from both sides thereof in the horizontal direction so as tosandwich them. The rotation axes of the pair of rollers 45 are orientedin the direction in which the plurality of main ropes 16 a are arranged.

FIGS. 47 and 48 are views illustrating another example of the vibrationdamping device 100. FIG. 47 is a side view of a vibration damping deviceaccording to Embodiment 3. FIG. 48 is a perspective view of thevibration damping device according to Embodiment 3. In this example, thestructure whose vibration is controlled by the vibration damping device100 is a single main rope 16.

The vibration damping device 100 includes a pair of roller units 41 fora first portion R1 and a second portion R2 of the main rope 16. Each ofthe pair of roller units 41 includes a box 41 a, a plurality of rollers41 c, and a pair of links 41 e.

The box 41 a of one of the pair of roller units 41 is arranged betweenone of a pair of outer magnet units 56 and an inner magnet unit 57. Thebox 41 a of the other of the pair of roller units 41 is arranged betweenthe other of the pair of outer magnet units 56 and the inner magnet unit57. Each box 41 a is a tubular member having openings at its top andbottom, for example. The box 41 a is formed of a ferromagnetic material.Alternatively, the box 41 a may have a ferromagnetic material attachedto its surface so as to have a ferromagnetic property.

Each of the plurality of rollers 41 c is arranged inside the box 41 a.The plurality of rollers 41 c include a pair of rollers arranged in theupper portion and a pair of rollers arranged in the lower portion of thebox 41 a, for example. The pair of rollers 41 c arranged in the upperportion of the box 41 a contact the main rope 16 from both sides thereofin the horizontal direction. The pair of rollers 41 c arranged in thelower portion of the box 41 a contact the main rope 16 from both sidesthereof in the horizontal direction. The plurality of rollers 41 c guidethe main rope 16 by rotating with respect to the vertical movement ofthe main rope 16 along with the movement of the car 14.

Each of the pair of links 41 e is a bar-like member. The pair of links41 e have joints 41 b at the upper ends thereof. The pair of links 41 erotatably support the box 41 a with the joints 41 b at the upper endsthereof. The pair of links 41 e also have joints 41 d at the lower endsthereof. The pair of links 41 e are rotatably supported on the housing40 with the joints 41 d at the lower ends thereof. The joints 41 b and41 d generate a frictional force against rotation. The pair of links 41e support the box 41 a such that the box 41 a is allowed to be displacedin the first direction in which the first portion R1 and the secondportion R2 are connected horizontally.

When the first portion R1 or the second portion R2 is displaced in thefirst direction due to vibration, the box 41 a is also displaced in thefirst direction through the plurality of rollers 41 c. The displacementin the first direction of the box 41 a having a ferromagnetic propertyis amplified with the magnetic forces from the outer magnet unit 56 andthe inner magnet unit 57. The box 41 a amplifies the displacement of themain rope 16 through the plurality of rollers 41 c.

When the box 41 a is displaced, the joints 41 b and 41 d rotate. At thistime, the kinetic energy about the joints 41 b and 41 d is dissipated asfrictional heat. Accordingly, the joints 41 b and 41 d function as avibration damper.

As described above, the vibration damping device 100 includes the pairof roller units 41. Each of the pair of roller units 41 is provided foreach of the first portion R1 and the second portion R2 of the main rope16. Each of the pair of roller units 41 includes the box 41 a, the pairof rollers 41 c, and the links 41 e. The box 41 a has a ferromagneticproperty. The box 41 a is arranged between one of the pair of outermagnet units 56 and the inner magnet unit 57. The pair of rollers 41 ccontact the main rope 16 from both sides thereof in the directionperpendicular to the main rope 16 inside the box 41 a. The links 41 esupport the box 41 a such that the box 41 a is allowed to be displacedin the first direction. Accordingly, the magnet units of thedisplacement amplifier 7 can amplify even a displacement of the mainrope 16 without a ferromagnetic property via the box 41 a with aferromagnetic property. The main rope 16 receives a force from thedisplacement amplifier 7 via the pair of rollers 41 c. Thus, wear of themain rope 16 is suppressed.

The links 41 e support the box 41 a via the rotatable joints. Thus, thelinks 41 e reduce vibration of the main rope 16 using friction thatoccurs along with the rotation of the joints. Accordingly, vibrationenergy is dissipated efficiently. Therefore, a high vibration dampingeffect can be obtained.

The pair of links 41 e may be supported on the housing 40 via ashock-absorbing material, such as a gel, for example. Alternatively, thepair of links 41 e may support the housing 40 via a shock-absorbingmaterial, such as a gel, for example.

FIGS. 49 and 50 are views illustrating another example of the vibrationdamping device 100. FIG. 49 is a perspective view of a vibration dampingdevice according to Embodiment 3. FIG. 50 is a top view of the vibrationdamping device according to Embodiment 3. In this example, the structurewhose vibration is controlled by the vibration damping device 100 is aplurality of main ropes 16.

The rotation axes of a pair of rollers 41 c are oriented in thedirection parallel with the direction in which the plurality of mainropes 16 are arranged. The pair of rollers 41 c contact each of theplurality of main ropes 16 from both sides thereof in the directionperpendicular to the rotation axes. Each of the pair of rollers 41 c hasgroove-like guides formed on its side face so as to maintain a constantdistance between each of the plurality of main ropes 16, which contactthe pair of rollers 41 c, in the horizontal direction.

As described above, when the target elevator rope is the plurality ofmain ropes 16 aligned in the horizontal direction, each roller 41 c hasa rotation axis parallel with the direction in which the plurality ofmain ropes 16 are aligned. Accordingly, each of the pair of roller units41 functions as a restraining member that maintains a constant distancebetween each of the plurality of main ropes 16, which would otherwisecontact each other, in the horizontal direction. This can suppress adecrease in the vibration damping performance due to variation in thetension of each of the plurality of main ropes 16.

FIG. 51 is a top view of a vibration damping device according toEmbodiment 3. FIG. 51 is a view illustrating another example of thevibration damping device 100. The vibration damping device 100 mayinclude a pair of magnet units 54 facing each other in the direction inwhich the plurality of main ropes 16 are arranged. Accordingly, thevibration damping device 100 can control vibration of the main ropes 16from two directions in the horizontal plane. It should be noted that thearrangement of the magnet units 54 in FIG. 51 is only exemplary, andthus the present invention is not limited thereto. For example, thevibration damping device 100 includes a plurality of magnet units 54. Insuch a case, the plurality of magnet units 54 may be arranged such thattheir magnetic poles face each of the pair of roller units 41 fromdifferent directions so as to surround them. The plurality of magnetunits 54 may be arranged at different heights along the longitudinaldirection of the main rope 16.

FIG. 52 are configuration views of an elevator apparatus according toEmbodiment 3. FIG. 52 are views illustrating another example of thevibration damping device 100. As illustrated in FIG. 52(a), thevibration damping device 100 is provided in the machine room 29. Asillustrated in FIG. 52(b), the main rope 16 is wound on the sheave ofthe traction machine 12 and the deflector sheave 13 that is a sheave.The first portion R1 of the main rope 16 is a portion drawn from thesheave of the traction machine 12, for example. The second portion R2 ofthe main rope 16 is a portion drawn from the sheave of the deflectorsheave 13, for example. In this manner, the main rope 16 may be wound onthe plurality of sheaves and folded thereover.

FIG. 53 is a side view of a vibration damping device according toEmbodiment 3. FIG. 53 is a view illustrating another example of thevibration damping device 100. The vibration damping device 100 controlsvibration of the compensating rope 17. The compensating rope 17 is woundon a compensating sheave 18 a and is folded thereover. The vibrationdamping device 100 is provided on a housing 18 b of the compensatingsheave 18 a.

FIG. 54 are configuration views of an elevator apparatus according toEmbodiment 3. FIG. 54 are views illustrating another example of thevibration damping device 100. The vibration damping device 100 controlsvibration of the governor rope 20. As illustrated in FIG. 54(a), thevibration damping device 100 is provided in the machine room 29. Asillustrated in FIG. 54(b), the governor rope 20 is wound on the sheaveof the governor 19. The vibration damping device 100 is provided belowthe governor 19.

INDUSTRIAL APPLICABILITY

The vibration damping device according to the present invention can beapplied to an elevator apparatus. The elevator apparatus according tothe present invention can be applied to a building with a plurality offloors.

REFERENCE SIGNS LIST

-   1, 1 a, 1 b, 1 c, 1 d, 1 e Structure-   2, 2 a, 2 b, 2 c Fixed plane-   3 Vibration force-   4 Damper-   5 a, 5 b Distance-   6 a, 6 b, 6 c Amplitude-   7 Displacement amplifier-   71 Negative stiffness portion-   8, 8 a, 8 b, 8 c, 8 d Limiting member-   9 Coupling portion-   10 Positive stiffness portion (Elastic body)-   11 Elevator apparatus-   12 Traction machine-   13 Deflector sheave-   14 Car-   15 Counterweight-   16, 16 a, 16 b Main rope-   17 Compensating rope-   18 Compensating sheave-   18 b Housing-   19 Governor-   20 Governor rope-   21 Governor tension sheave-   22 Traveling cable-   23 Building sway-   24, 24 a, 24 b permanent magnet-   25 Yoke-   26 Coil-   27 Electric resistor-   28 Machine room floor-   28 a Rope duct-   29 Machine room-   30 Fixation member-   31 Toggle link mechanism-   31 a Weight-   31 b Link-   31 c Rotation pivot-   32 Rope restraining member-   33 Linear guide-   34 Upper beam-   35 Shackle spring-   36 Shackle rod-   37 Ferromagnetic body-   38 Limiting member-   39 a Car suspension sheave-   39 b Counterweight suspension sheave-   40 Housing-   41 Roller unit-   41 a Box-   41 c Roller-   41 e Link-   41 b, 41 d Joint-   45 Roller-   46 Magnetic shield-   47 Magnetic body-   48 a Fixing portion-   48 b Hoistway-side terminal-   50 Support base-   51 Restraining member-   52 Base-   53 Roller-   54 Magnet unit-   55 Rope support-   56 Outer magnet unit-   57 Inner magnet unit-   58 Outer yoke-   59 Inner yoke-   60 a First outer permanent magnet-   60 b Second outer permanent magnet-   61 a First inner permanent magnet-   61 b Second inner permanent magnet

1. A vibration damping device for reducing vibration of a longstructure, comprising: a displacement amplifier arranged along a givenposition in a longitudinal direction of the structure, the displacementamplifier being configured to amplify a displacement of the structure;and a limiting member that controls displacement amplification performedby the displacement amplifier such that the displacement of thestructure amplified by the displacement amplifier does not becomegreater than a first displacement, the first displacement being thedisplacement of the structure by which the structure is not allowed toreturn to an equilibrium position of the vibration.
 2. The vibrationdamping device according to claim 1, wherein the displacement amplifieris arranged at a position where a distance between the displacementamplifier and a node of the vibration of the structure is shorter than adistance between the displacement amplifier and an antinode of thevibration of the structure and is greater than zero.
 3. The vibrationdamping device according to claim 1, wherein the displacement amplifierincludes a mechanical structure that exerts negative stiffness forapplying an elastic force, the elastic force being greater as thedisplacement of the structure is greater.
 4. The vibration dampingdevice according to claim 1, wherein the limiting member includes anelastic body with positive stiffness.
 5. The vibration damping deviceaccording to claim 1, wherein the limiting member controls displacementamplification performed by the displacement amplifier such that a forceexerted by the displacement amplifier does not exceed a force in adirection of the displacement of the structure generated due toequivalent stiffness between a fixed position of the structure and acoupled position of the structure where the displacement amplifieramplifies the displacement.
 6. The vibration damping device according toclaim 1, wherein the limiting member controls amplification of thedisplacement of the structure performed by the displacement amplifierbased on the first displacement as a displacement where a force exertedby the displacement amplifier exceeds a force in a direction of thedisplacement of the structure generated due to equivalent stiffnessbetween a fixed position of the structure and a coupled position of thestructure where the displacement amplifier amplifies the displacement ofthe structure.
 7. The vibration damping device according to claim 1,wherein the displacement amplifier applies a component of a force in adirection of the displacement of the vibration of the structure and thusin a direction of the displacement of the structure.
 8. The vibrationdamping device according to claim 1, further comprising a vibrationdamper that reduces the vibration of the structure.
 9. The vibrationdamping device according to claim 1, wherein when the structure is anelevator rope, the displacement amplifier is arranged along a givenposition in a longitudinal direction of the elevator rope, and amplifiesa displacement of the elevator rope, and the limiting member controlsdisplacement amplification performed by the displacement amplifier suchthat the displacement of the elevator rope amplified by the displacementamplifier does not become greater than the first displacement.
 10. Thevibration damping device according to claim 9, wherein the displacementamplifier is arranged at a position where a distance between thedisplacement amplifier and a node of the vibration of the elevator ropeis shorter than a distance between the displacement amplifier and anantinode of the vibration of the elevator rope and is greater than zero.11. The vibration damping device according to claim 9, wherein when theelevator rope is a main rope that is connected to a car and acounterweight of an elevator and is wound on a sheave, the displacementamplifier is arranged along a given position in a longitudinal directionof the main rope, and amplifies the displacement of the main rope, andthe limiting member controls displacement amplification performed by thedisplacement amplifier such that the displacement of the main ropeamplified by the displacement amplifier does not become greater than thefirst displacement.
 12. The vibration damping device according to claim11, wherein the displacement amplifier is arranged at a position where adistance between the displacement amplifier and the car, thecounterweight, or the sheave is shorter than a distance between thedisplacement amplifier and a midpoint between both fixed positions ofthe main rope and is greater than zero.
 13. The vibration damping deviceaccording to claim 11, wherein the limiting member controlsamplification of the displacement of the main rope performed by thedisplacement amplifier such that a force exerted by the displacementamplifier becomes smaller than a force with which the main rope attemptsto return to the equilibrium position with a tension of the main rope.14. The vibration damping device according to claim 11, wherein thedisplacement amplifier and the limiting member amplify the displacementof the main rope by exerting a force based on a modulus of elasticity Kthat satisfies an inequality:${{- \frac{T}{x_{0}}}\frac{L}{L - x_{o}}} < K < 0$ where T is a tensionof the main rope, x₀ is a distance from a connection point between thecar or the counterweight and the main rope to a position where thedisplacement amplifier is arranged, and L is the total length of themain rope.
 15. The vibration damping device according to claim 11,wherein the limiting member controls amplification of the displacementof the main rope performed by the displacement amplifier based on thefirst displacement as a displacement where a force is exerted with amodulus of elasticity that has a value obtained by dividing a tensionacting on the main rope when the car in an empty state is at a top floorof the elevator by a distance from a fixed position of the main rope toa position of the main rope coupled to the displacement amplifier. 16.The vibration damping device according to claim 9, wherein when theelevator rope is a plurality of main ropes that are connected to a carand a counterweight of an elevator and are wound on a sheave, thevibration damping device further comprises a restraining member thatmaintains a constant distance between each of the plurality of mainropes in a horizontal direction.
 17. The vibration damping deviceaccording to claim 16, wherein the restraining member is fixed to eachof the plurality of main ropes.
 18. The vibration damping deviceaccording to claim 16, wherein when the plurality of main ropes arealigned in the horizontal direction, the restraining member includes apair of rollers having rotation axes parallel with the direction inwhich the plurality of main ropes are aligned, the pair of rollers beingadapted to contact each of the plurality of main ropes from both sidesin a direction perpendicular to the rotation axes.
 19. The vibrationdamping device according to claim 9, wherein when the elevator rope is atraveling cable connected to a car of an elevator, the displacementamplifier is arranged along a given position in a longitudinal directionof the traveling cable, and amplifies a displacement of the travelingcable, and the limiting member controls displacement amplificationperformed by the displacement amplifier such that the displacement ofthe traveling cable amplified by the displacement amplifier does notbecome greater than the first displacement.
 20. The vibration dampingdevice according to claim 9, wherein the displacement amplifier includesa negative stiffness member that exerts a force corresponding to atransverse displacement of the elevator rope in a direction away fromthe equilibrium position of the elevator rope.
 21. The vibration dampingdevice according to claim 9, wherein: the displacement amplifierincludes at least one magnet unit, and the limiting member includes anon-magnetic body arranged between a magnetic pole of the magnet unitand the elevator rope.
 22. The vibration damping device according toclaim 9, wherein: the displacement amplifier includes a pair of magnetunits arranged such that magnetic poles of the pair of magnet units faceeach other across the elevator rope, and the limiting member includes apair of non-magnetic bodies arranged between the respective magneticpoles of the pair of magnet units and the elevator rope.
 23. Thevibration damping device according to claim 22, wherein the pair ofmagnet units are arranged such that same magnetic poles of the pair ofmagnet units face each other.
 24. The vibration damping device accordingto claim 22, wherein each of the pair of magnet units includes a yoke, afirst permanent magnet, and a second permanent magnet, the yoke beingarranged in a direction parallel with the elevator rope, the firstpermanent magnet having magnetic poles directed toward one end of theyoke from a direction of the elevator rope, and the second permanentmagnet having magnetic poles that are opposite to the magnetic poles ofthe first permanent magnet and directed toward another end of the yokefrom the same direction of the first permanent magnet.
 25. The vibrationdamping device according to claim 9, wherein the limiting memberincludes a roller adapted to contact the elevator rope.
 26. Thevibration damping device according to claim 9, wherein: the displacementamplifier includes an unstable link mechanism that generates a negativestiffness force utilizing a displacement of one or more links, and thelimiting member controls the displacement of at least one of the one ormore links.
 27. The vibration damping device according to claim 26,wherein the link mechanism is a pair of toggle link mechanisms arrangedacross the elevator rope.
 28. The vibration damping device according toclaim 9, wherein the displacement amplifier includes a roller adapted tocontact the elevator rope.
 29. The vibration damping device according toclaim 9, further comprising a vibration damper that reduces thevibration of the elevator rope.
 30. The vibration damping deviceaccording to claim 22, further comprising a vibration damper thatreduces the vibration of the elevator rope, wherein the vibration damperincludes a coil and an electrical resistor electrically connected to thecoil, the coil being adapted to pass a magnetic flux passing through atleast one of the pair of magnet units.
 31. The vibration damping deviceaccording to claim 24, further comprising a vibration damper thatreduces the vibration of the elevator rope, wherein the vibration damperincludes a coil and an electrical resistor electrically connected to thecoil, the coil being wound on the yoke of at least one of the pair ofmagnet units.
 32. An elevator apparatus comprising the vibration dampingdevice according to claim 9.